LMFDB - Embedded newform 384.2.v.a.37.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.295054 - 1.38309i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.82589 + 0.816174i) q^{4} +(-0.528754 + 0.433938i) q^{5} +(1.08069 - 0.912200i) q^{6} +(1.34993 - 0.901992i) q^{7} +(1.66758 + 2.28455i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(-0.295054 - 1.38309i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.82589 + 0.816174i) q^{4} +(-0.528754 + 0.433938i) q^{5} +(1.08069 - 0.912200i) q^{6} +(1.34993 - 0.901992i) q^{7} +(1.66758 + 2.28455i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(0.756187 + 0.603281i) q^{10} +(1.63279 + 5.38259i) q^{11} +(-1.58052 - 1.22555i) q^{12} +(-2.08146 + 2.53627i) q^{13} +(-1.64584 - 1.60094i) q^{14} +(-0.631952 - 0.261763i) q^{15} +(2.66772 - 2.98048i) q^{16} +(3.13903 - 1.30023i) q^{17} +(1.31392 + 0.523076i) q^{18} +(-4.93809 + 0.486360i) q^{19} +(0.611277 - 1.22388i) q^{20} +(1.43184 + 0.765333i) q^{21} +(6.96285 - 3.84646i) q^{22} +(9.20414 - 1.83082i) q^{23} +(-1.22870 + 2.54760i) q^{24} +(-0.884172 + 4.44503i) q^{25} +(4.12204 + 2.13052i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-1.72863 + 2.74871i) q^{28} +(8.34413 + 2.53116i) q^{29} +(-0.175582 + 0.951282i) q^{30} +(-1.13289 - 1.13289i) q^{31} +(-4.90940 - 2.81030i) q^{32} +(-3.97733 + 3.97733i) q^{33} +(-2.72452 - 3.95793i) q^{34} +(-0.322371 + 1.06272i) q^{35} +(0.335784 - 1.97161i) q^{36} +(0.101510 - 1.03065i) q^{37} +(2.12968 + 6.68633i) q^{38} +(-3.21799 - 0.640097i) q^{39} +(-1.87309 - 0.484342i) q^{40} +(0.931377 + 4.68235i) q^{41} +(0.636056 - 2.20618i) q^{42} +(2.71639 - 5.08201i) q^{43} +(-7.37442 - 8.49535i) q^{44} +(-0.0670457 - 0.680726i) q^{45} +(-5.24791 - 12.1900i) q^{46} +(-1.59064 - 3.84015i) q^{47} +(3.88610 + 0.947729i) q^{48} +(-1.67007 + 4.03191i) q^{49} +(6.40877 - 0.0886346i) q^{50} +(2.62643 + 2.15545i) q^{51} +(1.73048 - 6.32978i) q^{52} +(-9.08984 + 2.75737i) q^{53} +(0.158067 + 1.40535i) q^{54} +(-3.19905 - 2.13754i) q^{55} +(4.31176 + 1.57983i) q^{56} +(-2.75673 - 4.12574i) q^{57} +(1.03886 - 12.2875i) q^{58} +(-7.18814 - 8.75877i) q^{59} +(1.36752 - 0.0378333i) q^{60} +(-4.05732 + 2.16868i) q^{61} +(-1.23262 + 1.90115i) q^{62} +1.62354i q^{63} +(-2.43836 + 7.61934i) q^{64} -2.24429i q^{65} +(6.67454 + 4.32748i) q^{66} +(5.25582 - 2.80929i) q^{67} +(-4.67029 + 4.93606i) q^{68} +(5.95344 + 7.25428i) q^{69} +(1.56495 + 0.132310i) q^{70} +(-5.21854 - 7.81009i) q^{71} +(-2.82599 + 0.117312i) q^{72} +(-7.06162 - 4.71842i) q^{73} +(-1.45543 + 0.163700i) q^{74} +(-4.33697 + 1.31560i) q^{75} +(8.61944 - 4.91838i) q^{76} +(7.05920 + 5.79334i) q^{77} +(0.0641671 + 4.63964i) q^{78} +(2.16094 - 5.21696i) q^{79} +(-0.117226 + 2.73357i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(6.20131 - 2.66973i) q^{82} +(1.45381 + 14.7608i) q^{83} +(-3.23902 - 0.228782i) q^{84} +(-1.09556 + 2.04964i) q^{85} +(-7.83037 - 2.25755i) q^{86} +(1.70111 + 8.55204i) q^{87} +(-9.57400 + 12.7061i) q^{88} +(-5.09328 - 1.01312i) q^{89} +(-0.921725 + 0.293581i) q^{90} +(-0.522127 + 5.30124i) q^{91} +(-15.3114 + 10.8550i) q^{92} +(0.465078 - 1.53316i) q^{93} +(-4.84195 + 3.33305i) q^{94} +(2.39999 - 2.39999i) q^{95} +(0.164185 - 5.65447i) q^{96} +(-2.29352 - 2.29352i) q^{97} +(6.06926 + 1.12023i) q^{98} +(-5.38259 - 1.63279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.295054	−	1.38309i	−0.208635	−	0.977994i
$2$	−0.295054	−	1.38309i	−0.208635	−	0.977994i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$4$	−1.82589	+	0.816174i	−0.912943	+	0.408087i
$5$	−0.528754	+	0.433938i	−0.236466	+	0.194063i	−0.745162	−	0.666884i	$-0.767628\pi$
$5$	−0.528754	+	0.433938i	−0.236466	+	0.194063i	0.508696	+	0.860946i	$0.330128\pi$
$6$	1.08069	−	0.912200i	0.441190	−	0.372404i
$7$	1.34993	−	0.901992i	0.510224	−	0.340921i	−0.273661	−	0.961826i	$-0.588235\pi$
$7$	1.34993	−	0.901992i	0.510224	−	0.340921i	0.783886	+	0.620905i	$0.213235\pi$
$8$	1.66758	+	2.28455i	0.589578	+	0.807711i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	0.756187	+	0.603281i	0.239127	+	0.190774i
$11$	1.63279	+	5.38259i	0.492305	+	1.62291i	0.753374	+	0.657592i	$0.228425\pi$
$11$	1.63279	+	5.38259i	0.492305	+	1.62291i	−0.261069	+	0.965320i	$0.584075\pi$
$12$	−1.58052	−	1.22555i	−0.456256	−	0.353785i
$13$	−2.08146	+	2.53627i	−0.577294	+	0.703435i	−0.977007	−	0.213205i	$-0.931610\pi$
$13$	−2.08146	+	2.53627i	−0.577294	+	0.703435i	0.399713	+	0.916640i	$0.369110\pi$
$14$	−1.64584	−	1.60094i	−0.439869	−	0.427868i
$15$	−0.631952	−	0.261763i	−0.163169	−	0.0675869i
$16$	2.66772	−	2.98048i	0.666930	−	0.745120i
$17$	3.13903	−	1.30023i	0.761326	−	0.315352i	0.0319726	−	0.999489i	$-0.489821\pi$
$17$	3.13903	−	1.30023i	0.761326	−	0.315352i	0.729353	+	0.684137i	$0.239821\pi$
$18$	1.31392	+	0.523076i	0.309694	+	0.123290i
$19$	−4.93809	+	0.486360i	−1.13288	+	0.111579i	−0.647029	−	0.762465i	$-0.723989\pi$
$19$	−4.93809	+	0.486360i	−1.13288	+	0.111579i	−0.485847	+	0.874044i	$0.661489\pi$
$20$	0.611277	−	1.22388i	0.136686	−	0.273667i
$21$	1.43184	+	0.765333i	0.312452	+	0.167009i
$22$	6.96285	−	3.84646i	1.48449	−	0.820067i
$23$	9.20414	−	1.83082i	1.91920	−	0.381752i	0.919266	−	0.393637i	$-0.128783\pi$
$23$	9.20414	−	1.83082i	1.91920	−	0.381752i	0.999929	+	0.0118857i	$0.00378343\pi$
$24$	−1.22870	+	2.54760i	−0.250808	+	0.520027i
$25$	−0.884172	+	4.44503i	−0.176834	+	0.889007i
$26$	4.12204	+	2.13052i	0.808399	+	0.417829i
$27$	−0.995185	−	0.0980171i	−0.191523	−	0.0188634i
$28$	−1.72863	+	2.74871i	−0.326680	+	0.519457i
$29$	8.34413	+	2.53116i	1.54947	+	0.470025i	0.945127	−	0.326703i	$-0.105938\pi$
$29$	8.34413	+	2.53116i	1.54947	+	0.470025i	0.604338	+	0.796728i	$0.293438\pi$
$30$	−0.175582	+	0.951282i	−0.0320568	+	0.173679i
$31$	−1.13289	−	1.13289i	−0.203473	−	0.203473i	0.598013	−	0.801486i	$-0.295957\pi$
$31$	−1.13289	−	1.13289i	−0.203473	−	0.203473i	−0.801486	+	0.598013i	$0.795957\pi$
$32$	−4.90940	−	2.81030i	−0.867868	−	0.496795i
$33$	−3.97733	+	3.97733i	−0.692364	+	0.692364i
$34$	−2.72452	−	3.95793i	−0.467251	−	0.678779i
$35$	−0.322371	+	1.06272i	−0.0544907	+	0.179632i
$36$	0.335784	−	1.97161i	0.0559640	−	0.328602i
$37$	0.101510	−	1.03065i	0.0166882	−	0.169438i	−0.983228	−	0.182380i	$-0.941620\pi$
$37$	0.101510	−	1.03065i	0.0166882	−	0.169438i	0.999916	+	0.0129424i	$0.00411981\pi$
$38$	2.12968	+	6.68633i	0.345480	+	1.08467i
$39$	−3.21799	−	0.640097i	−0.515290	−	0.102498i
$40$	−1.87309	−	0.484342i	−0.296162	−	0.0765812i
$41$	0.931377	+	4.68235i	0.145457	+	0.731260i	0.982813	+	0.184603i	$0.0590999\pi$
$41$	0.931377	+	4.68235i	0.145457	+	0.731260i	−0.837357	+	0.546657i	$0.815900\pi$
$42$	0.636056	−	2.20618i	0.0981456	−	0.340420i
$43$	2.71639	−	5.08201i	0.414246	−	0.774999i	−0.585108	−	0.810956i	$-0.698948\pi$
$43$	2.71639	−	5.08201i	0.414246	−	0.774999i	0.999353	+	0.0359566i	$0.0114478\pi$
$44$	−7.37442	−	8.49535i	−1.11174	−	1.28072i
$45$	−0.0670457	−	0.680726i	−0.00999458	−	0.101477i
$46$	−5.24791	−	12.1900i	−0.773762	−	1.79731i
$47$	−1.59064	−	3.84015i	−0.232019	−	0.560143i	0.764396	−	0.644747i	$-0.223037\pi$
$47$	−1.59064	−	3.84015i	−0.232019	−	0.560143i	−0.996415	+	0.0846042i	$0.973037\pi$
$48$	3.88610	+	0.947729i	0.560911	+	0.136793i
$49$	−1.67007	+	4.03191i	−0.238582	+	0.575987i
$50$	6.40877	−	0.0886346i	0.906337	−	0.0125348i
$51$	2.62643	+	2.15545i	0.367773	+	0.301824i
$52$	1.73048	−	6.32978i	0.239974	−	0.877783i
$53$	−9.08984	+	2.75737i	−1.24858	+	0.378754i	−0.844296	−	0.535877i	$-0.819981\pi$
$53$	−9.08984	+	2.75737i	−1.24858	+	0.378754i	−0.404289	+	0.914631i	$0.632481\pi$
$54$	0.158067	+	1.40535i	0.0215102	+	0.191244i
$55$	−3.19905	−	2.13754i	−0.431360	−	0.288226i
$56$	4.31176	+	1.57983i	0.576183	+	0.211114i
$57$	−2.75673	−	4.12574i	−0.365138	−	0.546468i
$58$	1.03886	−	12.2875i	0.136409	−	1.61343i
$59$	−7.18814	−	8.75877i	−0.935816	−	1.14029i	−0.989901	−	0.141758i	$-0.954724\pi$
$59$	−7.18814	−	8.75877i	−0.935816	−	1.14029i	0.0540857	−	0.998536i	$-0.482776\pi$
$60$	1.36752	−	0.0378333i	0.176546	−	0.00488426i
$61$	−4.05732	+	2.16868i	−0.519486	+	0.277671i	−0.710231	−	0.703968i	$-0.751410\pi$
$61$	−4.05732	+	2.16868i	−0.519486	+	0.277671i	0.190745	+	0.981640i	$0.438910\pi$
$62$	−1.23262	+	1.90115i	−0.156544	+	0.241447i
$63$			1.62354i			0.204547i
$64$	−2.43836	+	7.61934i	−0.304795	+	0.952418i
$65$		−	2.24429i		−	0.278370i
$66$	6.67454	+	4.32748i	0.821579	+	0.532676i
$67$	5.25582	−	2.80929i	0.642101	−	0.343210i	−0.118002	−	0.993013i	$-0.537649\pi$
$67$	5.25582	−	2.80929i	0.642101	−	0.343210i	0.760102	+	0.649803i	$0.225149\pi$
$68$	−4.67029	+	4.93606i	−0.566356	+	0.598585i
$69$	5.95344	+	7.25428i	0.716709	+	0.873313i
$70$	1.56495	+	0.132310i	0.187047	+	0.0158141i
$71$	−5.21854	−	7.81009i	−0.619326	−	0.926887i	−0.999998	−	0.00217678i	$-0.999307\pi$
$71$	−5.21854	−	7.81009i	−0.619326	−	0.926887i	0.380671	−	0.924710i	$-0.375693\pi$
$72$	−2.82599	+	0.117312i	−0.333046	+	0.0138254i
$73$	−7.06162	−	4.71842i	−0.826500	−	0.552249i	0.0688430	−	0.997628i	$-0.478069\pi$
$73$	−7.06162	−	4.71842i	−0.826500	−	0.552249i	−0.895343	+	0.445378i	$0.853069\pi$
$74$	−1.45543	+	0.163700i	−0.169191	+	0.0190297i
$75$	−4.33697	+	1.31560i	−0.500790	+	0.151913i
$76$	8.61944	−	4.91838i	0.988717	−	0.564177i
$77$	7.05920	+	5.79334i	0.804471	+	0.660212i
$78$	0.0641671	+	4.63964i	0.00726549	+	0.525335i
$79$	2.16094	−	5.21696i	0.243124	−	0.586954i	−0.754466	−	0.656340i	$-0.772104\pi$
$79$	2.16094	−	5.21696i	0.243124	−	0.586954i	0.997590	+	0.0693857i	$0.0221039\pi$
$80$	−0.117226	+	2.73357i	−0.0131062	+	0.305622i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	6.20131	−	2.66973i	0.684820	−	0.294822i
$83$	1.45381	+	14.7608i	0.159576	+	1.62020i	0.657825	+	0.753170i	$0.271476\pi$
$83$	1.45381	+	14.7608i	0.159576	+	1.62020i	−0.498249	+	0.867034i	$0.666024\pi$
$84$	−3.23902	−	0.228782i	−0.353406	−	0.0249622i
$85$	−1.09556	+	2.04964i	−0.118830	+	0.222315i
$86$	−7.83037	−	2.25755i	−0.844370	−	0.243438i
$87$	1.70111	+	8.55204i	0.182378	+	0.916875i
$88$	−9.57400	+	12.7061i	−1.02059	+	1.35447i
$89$	−5.09328	−	1.01312i	−0.539887	−	0.107390i	−0.0823879	−	0.996600i	$-0.526255\pi$
$89$	−5.09328	−	1.01312i	−0.539887	−	0.107390i	−0.457499	+	0.889210i	$0.651255\pi$
$90$	−0.921725	+	0.293581i	−0.0971583	+	0.0309462i
$91$	−0.522127	+	5.30124i	−0.0547338	+	0.555721i
$92$	−15.3114	+	10.8550i	−1.59633	+	1.13172i
$93$	0.465078	−	1.53316i	0.0482264	−	0.158981i
$94$	−4.84195	+	3.33305i	−0.499409	+	0.343778i
$95$	2.39999	−	2.39999i	0.246234	−	0.246234i
$96$	0.164185	−	5.65447i	0.0167571	−	0.577107i
$97$	−2.29352	−	2.29352i	−0.232871	−	0.232871i	0.581019	−	0.813890i	$-0.302654\pi$
$97$	−2.29352	−	2.29352i	−0.232871	−	0.232871i	−0.813890	+	0.581019i	$0.802654\pi$
$98$	6.06926	+	1.12023i	0.613088	+	0.113160i
$99$	−5.38259	−	1.63279i	−0.540971	−	0.164102i
$100$	−2.01352	−	8.83776i	−0.201352	−	0.883776i
$101$	14.7112	+	1.44892i	1.46382	+	0.144173i	0.798322	−	0.602231i	$-0.205721\pi$
$101$	14.7112	+	1.44892i	1.46382	+	0.144173i	0.665493	+	0.746404i	$0.268221\pi$
$102$	2.20625	−	4.26856i	0.218451	−	0.422651i
$103$	2.66456	−	13.3956i	0.262546	−	1.31991i	−0.594260	−	0.804273i	$-0.702555\pi$
$103$	2.66456	−	13.3956i	0.262546	−	1.31991i	0.856807	−	0.515637i	$-0.172445\pi$
$104$	−9.26525	−	0.525781i	−0.908533	−	0.0515571i
$105$	−1.08920	+	0.216655i	−0.106295	+	0.0211433i
$106$	6.49569	+	11.7585i	0.630917	+	1.14209i
$107$	−11.9535	−	6.38925i	−1.15558	−	0.617672i	−0.221653	−	0.975126i	$-0.571145\pi$
$107$	−11.9535	−	6.38925i	−1.15558	−	0.617672i	−0.933931	+	0.357453i	$0.883645\pi$
$108$	1.89709	−	0.633276i	0.182548	−	0.0609370i
$109$	9.40784	−	0.926591i	0.901107	−	0.0887513i	0.363157	−	0.931728i	$-0.381699\pi$
$109$	9.40784	−	0.926591i	0.901107	−	0.0887513i	0.537950	+	0.842977i	$0.319199\pi$
$110$	−2.01252	+	5.05527i	−0.191886	+	0.482001i
$111$	0.956804	−	0.396321i	0.0908158	−	0.0376171i
$112$	0.912855	−	6.42969i	0.0862566	−	0.607549i
$113$	11.6656	+	4.83206i	1.09741	+	0.454562i	0.856585	−	0.516006i	$-0.172582\pi$
$113$	11.6656	+	4.83206i	1.09741	+	0.454562i	0.240825	+	0.970569i	$0.422582\pi$
$114$	−4.89289	+	5.03013i	−0.458261	+	0.471115i
$115$	−4.07227	+	4.96207i	−0.379741	+	0.462716i
$116$	−17.3013	+	2.18864i	−1.60638	+	0.203211i
$117$	−0.952433	−	3.13975i	−0.0880525	−	0.290270i
$118$	−9.99329	+	12.5262i	−0.919957	+	1.15313i
$119$	3.06466	−	4.58659i	0.280937	−	0.420452i
$120$	−0.455818	−	1.88024i	−0.0416103	−	0.171641i
$121$	−17.1601	+	11.4660i	−1.56001	+	1.04236i
$122$	4.19661	+	4.97176i	0.379944	+	0.450122i
$123$	−3.69041	+	3.02864i	−0.332753	+	0.273084i
$124$	2.99316	+	1.14389i	0.268794	+	0.102724i
$125$	−3.07358	−	5.75026i	−0.274909	−	0.514319i
$126$	2.24551	−	0.479033i	0.200046	−	0.0426757i
$127$	9.22802			0.818854			0.409427	−	0.912343i	$-0.365729\pi$
$127$	9.22802			0.818854			0.409427	+	0.912343i	$0.365729\pi$
$128$	11.2577	+	1.12436i	0.995050	+	0.0993800i
$129$	5.76243			0.507353
$130$	−3.10406	+	0.662187i	−0.272244	+	0.0580777i
$131$	0.386464	+	0.723023i	0.0337655	+	0.0631708i	0.898238	−	0.439509i	$-0.144848\pi$
$131$	0.386464	+	0.723023i	0.0337655	+	0.0631708i	−0.864473	+	0.502680i	$0.832348\pi$
$132$	4.01596	−	10.5083i	0.349544	−	0.914634i
$133$	−6.22737	+	5.11067i	−0.539981	+	0.443151i
$134$	−5.43626	−	6.44039i	−0.469622	−	0.556365i
$135$	0.568742	−	0.380021i	0.0489495	−	0.0327070i
$136$	8.20501	+	5.00304i	0.703574	+	0.429007i
$137$	3.19197	−	4.77712i	0.272708	−	0.408137i	−0.669684	−	0.742646i	$-0.733570\pi$
$137$	3.19197	−	4.77712i	0.272708	−	0.408137i	0.942393	+	0.334509i	$0.108570\pi$
$138$	8.27675	−	10.3746i	0.704564	−	0.883141i
$139$	−6.33425	−	20.8812i	−0.537264	−	1.77112i	−0.631283	−	0.775553i	$-0.717471\pi$
$139$	−6.33425	−	20.8812i	−0.537264	−	1.77112i	0.0940186	−	0.995570i	$-0.470029\pi$
$140$	−0.278748	−	2.20351i	−0.0235585	−	0.186231i
$141$	2.63688	−	3.21305i	0.222066	−	0.270588i
$142$	−9.26232	+	9.52211i	−0.777277	+	0.799078i
$143$	−17.0503	−	7.06247i	−1.42582	−	0.590593i
$144$	0.996074	+	3.87399i	0.0830062	+	0.322833i
$145$	−5.51036	+	2.28247i	−0.457611	+	0.189548i
$146$	−4.44245	+	11.1591i	−0.367660	+	0.923530i
$147$	−4.34309	+	0.427757i	−0.358212	+	0.0352808i
$148$	0.655844	+	1.96470i	0.0539100	+	0.161497i
$149$	−5.29971	−	2.83276i	−0.434170	−	0.232068i	0.239808	−	0.970820i	$-0.422916\pi$
$149$	−5.29971	−	2.83276i	−0.434170	−	0.232068i	−0.673977	+	0.738752i	$0.735416\pi$
$150$	3.09924	+	5.61025i	0.253052	+	0.458075i
$151$	3.77787	−	0.751466i	0.307439	−	0.0611534i	−0.0389598	−	0.999241i	$-0.512404\pi$
$151$	3.77787	−	0.751466i	0.307439	−	0.0611534i	0.346399	+	0.938087i	$0.387404\pi$
$152$	−9.34577	−	10.4703i	−0.758042	−	0.849252i
$153$	−0.662850	+	3.33237i	−0.0535883	+	0.269406i
$154$	5.92987	−	11.4729i	0.477842	−	0.924510i
$155$	1.09062	+	0.107417i	0.0876009	+	0.00862794i
$156$	6.39811	−	1.45769i	0.512259	−	0.116709i
$157$	17.0726	+	5.17892i	1.36254	+	0.413323i	0.885125	−	0.465354i	$-0.154073\pi$
$157$	17.0726	+	5.17892i	1.36254	+	0.413323i	0.477418	+	0.878677i	$0.341573\pi$
$158$	−7.85313	−	1.44949i	−0.624761	−	0.115315i
$159$	−6.71670	−	6.71670i	−0.532669	−	0.532669i
$160$	3.81536	−	0.644417i	0.301631	−	0.0509456i
$161$	10.7735	−	10.7735i	0.849073	−	0.849073i
$162$	−1.16490	+	0.801881i	−0.0915230	+	0.0630017i
$163$	−1.42526	+	4.69846i	−0.111635	+	0.368012i	−0.994900	−	0.100862i	$-0.967840\pi$
$163$	−1.42526	+	4.69846i	−0.111635	+	0.368012i	0.883265	+	0.468874i	$0.155340\pi$
$164$	−5.52220	−	7.78927i	−0.431211	−	0.608240i
$165$	0.377118	−	3.82894i	0.0293586	−	0.298083i
$166$	19.9865	−	6.36598i	1.55126	−	0.494096i
$167$	13.0664	+	2.59906i	1.01111	+	0.201122i	0.672729	−	0.739889i	$-0.265122\pi$
$167$	13.0664	+	2.59906i	1.01111	+	0.201122i	0.338377	+	0.941011i	$0.390122\pi$
$168$	0.639258	+	4.54736i	0.0493199	+	0.350836i
$169$	0.435994	+	2.19189i	0.0335380	+	0.168607i
$170$	3.15809	+	0.910500i	0.242215	+	0.0698322i
$171$	2.33906	−	4.37608i	0.178873	−	0.334647i
$172$	−0.812015	+	11.4962i	−0.0619156	+	0.876578i
$173$	−1.01311	−	10.2862i	−0.0770250	−	0.782048i	−0.953659	−	0.300890i	$-0.902716\pi$
$173$	−1.01311	−	10.2862i	−0.0770250	−	0.782048i	0.876634	−	0.481158i	$-0.159784\pi$
$174$	11.3263	−	4.87610i	0.858648	−	0.369657i
$175$	2.81582	+	6.79799i	0.212856	+	0.513879i
$176$	20.3985	+	9.49274i	1.53760	+	0.715542i
$177$	4.33608	−	10.4682i	0.325920	−	0.786840i
$178$	0.101561	+	7.34340i	0.00761230	+	0.550411i
$179$	18.6867	+	15.3357i	1.39671	+	1.14625i	0.970353	+	0.241691i	$0.0777020\pi$
$179$	18.6867	+	15.3357i	1.39671	+	1.14625i	0.426353	+	0.904557i	$0.359798\pi$
$180$	0.678009	+	1.18821i	0.0505358	+	0.0885637i
$181$	4.78750	−	1.45227i	0.355852	−	0.107946i	−0.107297	−	0.994227i	$-0.534220\pi$
$181$	4.78750	−	1.45227i	0.355852	−	0.107946i	0.463149	+	0.886281i	$0.346720\pi$
$182$	7.48616	−	0.842005i	0.554911	−	0.0624136i
$183$	−3.82521	−	2.55593i	−0.282768	−	0.188939i
$184$	19.5312	+	17.9743i	1.43986	+	1.32508i
$185$	0.393564	+	0.589010i	0.0289354	+	0.0433049i
$186$	−2.25772	−	0.190881i	−0.165544	−	0.0139961i
$187$	12.1240	+	14.7731i	0.886592	+	1.08032i
$188$	6.03856	+	5.71343i	0.440407	+	0.416695i
$189$	−1.43184	+	0.765333i	−0.104151	+	0.0556698i
$190$	−4.02753	−	2.61128i	−0.292188	−	0.189442i
$191$		−	15.9075i		−	1.15102i	−0.817794	−	0.575511i	$-0.804803\pi$
$191$		−	15.9075i		−	1.15102i	0.817794	−	0.575511i	$-0.195197\pi$
$192$	−7.86910	+	1.44129i	−0.567903	+	0.104016i
$193$		−	6.01093i		−	0.432676i	−0.976319	−	0.216338i	$-0.930589\pi$
$193$		−	6.01093i		−	0.432676i	0.976319	−	0.216338i	$-0.0694113\pi$
$194$	−2.49543	+	3.84886i	−0.179162	+	0.276332i
$195$	1.97929	−	1.05795i	0.141740	−	0.0757615i
$196$	−0.241380	−	8.72488i	−0.0172414	−	0.623206i
$197$	−4.53349	−	5.52407i	−0.322998	−	0.393574i	0.586044	−	0.810279i	$-0.300685\pi$
$197$	−4.53349	−	5.52407i	−0.322998	−	0.393574i	−0.909042	+	0.416705i	$0.863185\pi$
$198$	−0.670144	+	7.92638i	−0.0476250	+	0.563303i
$199$	0.582864	+	0.872318i	0.0413181	+	0.0618370i	0.851554	−	0.524268i	$-0.175661\pi$
$199$	0.582864	+	0.872318i	0.0413181	+	0.0618370i	−0.810235	+	0.586104i	$0.800661\pi$
$200$	−11.6293	+	5.39251i	−0.822318	+	0.381308i
$201$	4.95515	+	3.31093i	0.349510	+	0.233535i
$202$	−2.33660	−	20.7744i	−0.164402	−	1.46168i
$203$	13.5470	−	4.10945i	0.950816	−	0.288427i
$204$	−6.55478	−	1.79199i	−0.458926	−	0.125464i
$205$	−2.52432	−	2.07165i	−0.176306	−	0.144691i
$206$	−19.3136	+	0.267111i	−1.34564	+	0.0186105i
$207$	−3.59128	+	8.67011i	−0.249611	+	0.602614i
$208$	2.00655	+	12.9698i	0.139129	+	0.899296i
$209$	−10.6807	−	25.7856i	−0.738803	−	1.78363i
$210$	0.621025	+	1.44253i	0.0428548	+	0.0995443i
$211$	0.198977	+	2.02024i	0.0136981	+	0.139079i	0.999601	−	0.0282379i	$-0.00898959\pi$
$211$	0.198977	+	2.02024i	0.0136981	+	0.139079i	−0.985903	+	0.167317i	$0.946490\pi$
$212$	14.3465	−	12.4535i	0.985322	−	0.855312i
$213$	4.42788	−	8.28399i	0.303394	−	0.567610i
$214$	−5.31001	+	18.4179i	−0.362985	+	1.25902i
$215$	0.768971	+	3.86588i	0.0524434	+	0.263651i
$216$	−1.43562	−	2.43700i	−0.0976818	−	0.165817i
$217$	−2.55117	−	0.507460i	−0.173185	−	0.0344486i
$218$	−4.05738	−	12.7385i	−0.274801	−	0.862760i
$219$	0.832453	−	8.45204i	0.0562520	−	0.571136i
$220$	7.58571	+	1.29192i	0.511428	+	0.0871011i
$221$	−3.23604	+	10.6678i	−0.217680	+	0.717594i
$222$	−0.830458	−	1.20641i	−0.0557367	−	0.0809690i
$223$	7.02475	−	7.02475i	0.470412	−	0.470412i	−0.431636	−	0.902048i	$-0.642064\pi$
$223$	7.02475	−	7.02475i	0.470412	−	0.470412i	0.902048	+	0.431636i	$0.142064\pi$
$224$	−9.16220	+	0.634546i	−0.612175	+	0.0423974i
$225$	−3.20469	−	3.20469i	−0.213646	−	0.213646i
$226$	3.24119	−	17.5604i	0.215601	−	1.16810i
$227$	17.1910	+	5.21483i	1.14101	+	0.346121i	0.803560	−	0.595224i	$-0.202937\pi$
$227$	17.1910	+	5.21483i	1.14101	+	0.346121i	0.337447	+	0.941345i	$0.390437\pi$
$228$	8.40080	+	5.28316i	0.556357	+	0.349886i
$229$	−1.86115	−	0.183308i	−0.122988	−	0.0121133i	0.0363356	−	0.999340i	$-0.488431\pi$
$229$	−1.86115	−	0.183308i	−0.122988	−	0.0121133i	−0.159324	+	0.987226i	$0.550931\pi$
$230$	8.06454	+	4.16824i	0.531760	+	0.274846i
$231$	−1.78158	+	8.95662i	−0.117220	+	0.589302i
$232$	8.13192	+	23.2835i	0.533886	+	1.52864i
$233$	5.61575	−	1.11704i	0.367900	−	0.0731799i	−0.00767818	−	0.999971i	$-0.502444\pi$
$233$	5.61575	−	1.11704i	0.367900	−	0.0731799i	0.375578	+	0.926791i	$0.377444\pi$
$234$	−4.06154	+	2.24370i	−0.265511	+	0.146675i
$235$	2.50744	+	1.34026i	0.163568	+	0.0874287i
$236$	20.2734	+	10.1257i	1.31969	+	0.659130i
$237$	5.61961	−	0.553483i	0.365033	−	0.0359526i
$238$	−7.24792	−	2.88542i	−0.469813	−	0.187034i
$239$	−4.95194	+	2.05116i	−0.320315	+	0.132679i	−0.537047	−	0.843552i	$-0.680460\pi$
$239$	−4.95194	+	2.05116i	−0.320315	+	0.132679i	0.216732	+	0.976231i	$0.430460\pi$
$240$	−2.46605	+	1.18521i	−0.159183	+	0.0765050i
$241$	−26.2342	−	10.8666i	−1.68989	−	0.699977i	−0.690174	−	0.723644i	$-0.742466\pi$
$241$	−26.2342	−	10.8666i	−1.68989	−	0.699977i	−0.999720	+	0.0236668i	$0.992466\pi$
$242$	20.9217	+	20.3509i	1.34490	+	1.30821i
$243$	0.634393	−	0.773010i	0.0406963	−	0.0495886i
$244$	5.63818	−	7.27124i	0.360947	−	0.465494i
$245$	−0.866539	−	2.85660i	−0.0553612	−	0.182501i
$246$	5.27777	+	4.21057i	0.336498	+	0.268456i
$247$	9.04492	−	13.5367i	0.575515	−	0.861318i
$248$	0.698962	−	4.47732i	0.0443841	−	0.284310i
$249$	−12.3325	+	8.24032i	−0.781541	+	0.522209i
$250$	−7.04627	+	5.94768i	−0.445645	+	0.376165i
$251$	3.30209	−	2.70996i	0.208426	−	0.171051i	−0.524389	−	0.851479i	$-0.675706\pi$
$251$	3.30209	−	2.70996i	0.208426	−	0.171051i	0.732815	+	0.680428i	$0.238206\pi$
$252$	−1.32509	−	2.96440i	−0.0834731	−	0.186740i
$253$	24.8830	+	46.5527i	1.56438	+	2.92675i
$254$	−2.72276	−	12.7632i	−0.170841	−	0.800834i
$255$	−2.32407			−0.145539
$256$	−1.76654	−	15.9022i	−0.110409	−	0.993886i
$257$	−2.10746			−0.131460			−0.0657299	−	0.997837i	$-0.520938\pi$
$257$	−2.10746			−0.131460			−0.0657299	+	0.997837i	$0.520938\pi$
$258$	−1.70023	−	7.96997i	−0.105852	−	0.496188i
$259$	−0.792607	−	1.48286i	−0.0492502	−	0.0921406i
$260$	1.83173	+	4.09782i	0.113599	+	0.254136i
$261$	−6.74033	+	5.53165i	−0.417216	+	0.342400i
$262$	0.885979	−	0.747846i	0.0547360	−	0.0462021i
$263$	−7.93864	+	5.30443i	−0.489518	+	0.327085i	−0.775713	−	0.631086i	$-0.782609\pi$
$263$	−7.93864	+	5.30443i	−0.489518	+	0.327085i	0.286195	+	0.958171i	$0.407609\pi$
$264$	−15.7189	−	2.45391i	−0.967433	−	0.151027i
$265$	3.60976	−	5.40239i	0.221746	−	0.331866i
$266$	8.90594	+	7.10510i	0.546058	+	0.435642i
$267$	−1.50747	−	4.96945i	−0.0922555	−	0.304126i
$268$	−7.30366	+	9.41912i	−0.446142	+	0.575364i
$269$	5.67648	−	6.91681i	0.346101	−	0.421725i	−0.570644	−	0.821197i	$-0.693307\pi$
$269$	5.67648	−	6.91681i	0.346101	−	0.421725i	0.916745	+	0.399472i	$0.130807\pi$
$270$	−0.693414	−	0.674495i	−0.0421998	−	0.0410485i
$271$	−16.6537	−	6.89819i	−1.01164	−	0.419035i	−0.185587	−	0.982628i	$-0.559419\pi$
$271$	−16.6537	−	6.89819i	−1.01164	−	0.419035i	−0.826053	+	0.563593i	$0.809419\pi$
$272$	4.49874	−	12.8245i	0.272776	−	0.777597i
$273$	−4.92141	+	2.03851i	−0.297857	+	0.123377i
$274$	−7.54900	−	3.00528i	−0.456052	−	0.181555i
$275$	−25.3695	+	2.49867i	−1.52984	+	0.150676i
$276$	−16.7911	−	8.38645i	−1.01070	−	0.504805i
$277$	−26.6667	−	14.2536i	−1.60225	−	0.856418i	−0.998232	−	0.0594445i	$-0.981067\pi$
$277$	−26.6667	−	14.2536i	−1.60225	−	0.856418i	−0.604014	−	0.796974i	$-0.706433\pi$
$278$	−27.0117	+	14.9219i	−1.62006	+	0.894959i
$279$	1.57136	−	0.312563i	0.0940749	−	0.0187127i
$280$	−2.96541	+	1.03569i	−0.177217	+	0.0618942i
$281$	1.06037	−	5.33086i	0.0632566	−	0.318012i	−0.936182	−	0.351516i	$-0.885666\pi$
$281$	1.06037	−	5.33086i	0.0632566	−	0.318012i	0.999439	+	0.0335034i	$0.0106664\pi$
$282$	−5.22197	−	2.69903i	−0.310964	−	0.160725i
$283$	−0.974573	−	0.0959871i	−0.0579323	−	0.00570584i	0.0690094	−	0.997616i	$-0.478016\pi$
$283$	−0.974573	−	0.0959871i	−0.0579323	−	0.00570584i	−0.126942	+	0.991910i	$0.540516\pi$
$284$	15.9028	+	10.0011i	0.943660	+	0.593456i
$285$	3.24795	+	0.985254i	0.192392	+	0.0583614i
$286$	−4.73728	+	25.6659i	−0.280121	+	1.51766i
$287$	5.48073	+	5.48073i	0.323517	+	0.323517i
$288$	5.06419	−	2.52070i	0.298411	−	0.148534i
$289$	−3.85791	+	3.85791i	−0.226936	+	0.226936i
$290$	4.78272	+	6.94788i	0.280851	+	0.407994i
$291$	0.941545	−	3.10386i	0.0551943	−	0.181951i
$292$	16.7448	+	2.85179i	0.979913	+	0.166888i
$293$	−0.115596	+	1.17366i	−0.00675318	+	0.0685662i	−0.997971	−	0.0636759i	$-0.979718\pi$
$293$	−0.115596	+	1.17366i	−0.00675318	+	0.0685662i	0.991217	+	0.132242i	$0.0422176\pi$
$294$	1.87308	+	5.88069i	0.109240	+	0.342969i
$295$	7.60152	+	1.51204i	0.442577	+	0.0880341i
$296$	2.52385	−	1.48679i	0.146696	−	0.0864176i
$297$	−1.09734	−	5.51671i	−0.0636743	−	0.320112i
$298$	−2.35426	+	8.16581i	−0.136379	+	0.473033i
$299$	−14.5146	+	27.1550i	−0.839403	+	1.57041i
$300$	6.84504	−	5.94186i	0.395199	−	0.343054i
$301$	−0.917004	−	9.31050i	−0.0528552	−	0.536648i
$302$	−2.15402	−	5.00342i	−0.123950	−	0.287915i
$303$	5.65696	+	13.6571i	0.324984	+	0.784580i
$304$	−11.7239	+	16.0154i	−0.672409	+	0.918544i
$305$	1.20425	−	2.90732i	0.0689553	−	0.166473i
$306$	4.80456	−	0.0664480i	0.274658	−	0.00379858i
$307$	−2.88154	−	2.36482i	−0.164458	−	0.134967i	0.548565	−	0.836108i	$-0.315174\pi$
$307$	−2.88154	−	2.36482i	−0.164458	−	0.134967i	−0.713023	+	0.701141i	$0.752674\pi$
$308$	−17.6177	−	4.81643i	−1.00386	−	0.274442i
$309$	13.0699	−	3.96473i	0.743523	−	0.225545i
$310$	−0.173225	−	1.54012i	−0.00983853	−	0.0874732i
$311$	−1.89213	−	1.26428i	−0.107293	−	0.0716908i	0.500766	−	0.865583i	$-0.333052\pi$
$311$	−1.89213	−	1.26428i	−0.107293	−	0.0716908i	−0.608059	+	0.793892i	$0.708052\pi$
$312$	−3.90391	−	8.41907i	−0.221015	−	0.476636i
$313$	3.72555	+	5.57567i	0.210580	+	0.315156i	0.921691	−	0.387924i	$-0.126808\pi$
$313$	3.72555	+	5.57567i	0.210580	+	0.315156i	−0.711111	+	0.703080i	$0.751808\pi$
$314$	2.12558	−	25.1410i	0.119953	−	1.41879i
$315$	−0.704516	−	0.858455i	−0.0396950	−	0.0483685i
$316$	0.312326	+	11.2893i	0.0175697	+	0.635071i
$317$	−10.4983	+	5.61143i	−0.589641	+	0.315169i	−0.739097	−	0.673599i	$-0.764748\pi$
$317$	−10.4983	+	5.61143i	−0.589641	+	0.315169i	0.149457	+	0.988768i	$0.452248\pi$
$318$	−7.30803	+	11.2716i	−0.409814	+	0.632080i
$319$			49.0459i			2.74604i
$320$	−2.01703	−	5.08686i	−0.112755	−	0.284364i
$321$		−	13.5539i		−	0.756504i
$322$	−18.0796	−	11.7220i	−1.00753	−	0.653242i
$323$	−14.8684	+	7.94734i	−0.827301	+	0.442202i
$324$	1.45278	+	1.37456i	0.0807102	+	0.0763646i
$325$	−9.43344	−	11.4947i	−0.523273	−	0.637610i
$326$	6.91893	+	0.584969i	0.383204	+	0.0323984i
$327$	5.25200	+	7.86018i	0.290436	+	0.434669i
$328$	−9.14393	+	9.93597i	−0.504889	+	0.548622i
$329$	−5.61103	−	3.74917i	−0.309346	−	0.206699i
$330$	−5.40705	+	0.608157i	−0.297648	+	0.0334779i
$331$	9.14852	−	2.77517i	0.502848	−	0.152537i	−0.0286622	−	0.999589i	$-0.509125\pi$
$331$	9.14852	−	2.77517i	0.502848	−	0.152537i	0.531510	+	0.847052i	$0.321625\pi$
$332$	−14.7018	−	25.7649i	−0.806868	−	1.41403i
$333$	0.800558	+	0.657001i	0.0438703	+	0.0360034i
$334$	−0.260545	−	18.8389i	−0.0142564	−	1.03082i
$335$	−1.55998	+	3.76612i	−0.0852308	+	0.205765i
$336$	6.10080	−	2.22587i	0.332826	−	0.121431i
$337$	−1.36566	−	3.29699i	−0.0743922	−	0.179599i	0.882309	−	0.470671i	$-0.155988\pi$
$337$	−1.36566	−	3.29699i	−0.0743922	−	0.179599i	−0.956701	+	0.291072i	$0.905988\pi$
$338$	2.90295	−	1.24975i	0.157899	−	0.0679773i
$339$	1.23764	+	12.5660i	0.0672194	+	0.682490i
$340$	0.327497	−	4.63658i	0.0177610	−	0.251454i
$341$	4.24810	−	7.94764i	0.230048	−	0.430389i
$342$	−6.74267	−	1.94396i	−0.364602	−	0.105117i
$343$	3.59944	+	18.0956i	0.194351	+	0.977071i
$344$	16.1399	−	2.26891i	0.870205	−	0.122332i
$345$	−6.29581	−	1.25231i	−0.338955	−	0.0674224i
$346$	−13.9279	+	4.43622i	−0.748768	+	0.238492i
$347$	−2.80565	+	28.4863i	−0.150615	+	1.52922i	0.561687	+	0.827350i	$0.310152\pi$
$347$	−2.80565	+	28.4863i	−0.150615	+	1.52922i	−0.712302	+	0.701873i	$0.752348\pi$
$348$	−10.0860	−	14.2267i	−0.540666	−	0.762629i
$349$	1.72452	−	5.68498i	0.0923115	−	0.304310i	−0.898611	−	0.438747i	$-0.855422\pi$
$349$	1.72452	−	5.68498i	0.0923115	−	0.304310i	0.990922	+	0.134437i	$0.0429225\pi$
$350$	8.57142	−	5.90031i	0.458162	−	0.315385i
$351$	2.32004	−	2.32004i	0.123835	−	0.123835i
$352$	7.11065	−	31.0139i	0.378999	−	1.65305i
$353$	19.0555	+	19.0555i	1.01422	+	1.01422i	0.999897	+	0.0143267i	$0.00456050\pi$
$353$	19.0555	+	19.0555i	1.01422	+	1.01422i	0.0143267	+	0.999897i	$0.495439\pi$
$354$	−15.7579	−	2.90850i	−0.837523	−	0.154585i
$355$	6.14841	+	1.86510i	0.326324	+	0.0989893i
$356$	10.1266	−	2.30717i	0.536710	−	0.122280i
$357$	5.48968	+	0.540687i	0.290545	+	0.0286162i
$358$	15.6972	−	30.3702i	0.829621	−	1.60512i
$359$	2.35704	−	11.8497i	0.124400	−	0.625401i	−0.867401	−	0.497610i	$-0.834211\pi$
$359$	2.35704	−	11.8497i	0.124400	−	0.625401i	0.991801	−	0.127791i	$-0.0407888\pi$
$360$	1.44335	−	1.28833i	0.0760712	−	0.0679012i
$361$	5.51328	−	1.09666i	0.290173	−	0.0577190i
$362$	−3.42120	−	6.19305i	−0.179814	−	0.325499i
$363$	−18.2013	−	9.72882i	−0.955322	−	0.510630i
$364$	−3.37339	−	10.1056i	−0.176814	−	0.529678i
$365$	5.78136	−	0.569414i	0.302610	−	0.0298045i
$366$	−2.40643	+	6.04476i	−0.125786	+	0.315964i
$367$	−25.4089	+	10.5247i	−1.32633	+	0.549385i	−0.929607	−	0.368553i	$-0.879853\pi$
$367$	−25.4089	+	10.5247i	−1.32633	+	0.549385i	−0.396725	+	0.917937i	$0.629853\pi$
$368$	19.0973	−	32.3169i	0.995518	−	1.68463i
$369$	−4.41068	−	1.82696i	−0.229611	−	0.0951078i
$370$	0.698532	−	0.718125i	0.0363150	−	0.0373335i
$371$	−9.78348	+	11.9212i	−0.507933	+	0.618918i
$372$	0.402144	+	3.17896i	0.0208502	+	0.164821i
$373$	−0.408544	−	1.34679i	−0.0211536	−	0.0697340i	0.945728	−	0.324959i	$-0.105350\pi$
$373$	−0.408544	−	1.34679i	−0.0211536	−	0.0697340i	−0.966882	+	0.255225i	$0.917850\pi$
$374$	16.8553	−	21.1274i	0.871568	−	1.09247i
$375$	3.62240	−	5.42131i	0.187060	−	0.279955i
$376$	6.12050	−	10.0377i	0.315641	−	0.517652i
$377$	−23.7877	+	15.8944i	−1.22513	+	0.818605i
$378$	1.48100	+	1.75455i	0.0761742	+	0.0902442i
$379$	23.7046	−	19.4539i	1.21762	−	0.999279i	0.217896	−	0.975972i	$-0.430081\pi$
$379$	23.7046	−	19.4539i	1.21762	−	0.999279i	0.999728	−	0.0233068i	$-0.00741947\pi$
$380$	−2.42330	+	6.34091i	−0.124312	+	0.325282i
$381$	4.35006	+	8.13838i	0.222860	+	0.416942i
$382$	−22.0015	+	4.69356i	−1.12569	+	0.240143i
$383$	8.64642			0.441812			0.220906	−	0.975295i	$-0.429099\pi$
$383$	8.64642			0.441812			0.220906	+	0.975295i	$0.429099\pi$
$384$	4.31525	+	10.4584i	0.220212	+	0.533704i
$385$	−6.24653			−0.318353
$386$	−8.31367	+	1.77355i	−0.423155	+	0.0902713i
$387$	2.71639	+	5.08201i	0.138082	+	0.258333i
$388$	6.05961	+	2.31579i	0.307630	+	0.117566i
$389$	−1.33453	+	1.09522i	−0.0676634	+	0.0555299i	−0.667617	−	0.744505i	$-0.732686\pi$
$389$	−1.33453	+	1.09522i	−0.0676634	+	0.0555299i	0.599954	+	0.800035i	$0.295186\pi$
$390$	−2.04724	−	2.42538i	−0.103666	−	0.122814i
$391$	26.5116	−	17.7145i	1.34075	−	0.895859i
$392$	−11.9961	+	2.90816i	−0.605894	+	0.146884i
$393$	−0.455471	+	0.681661i	−0.0229755	+	0.0343853i
$394$	−6.30268	+	7.90013i	−0.317524	+	0.398003i
$395$	1.12123	+	3.69620i	0.0564152	+	0.185976i
$396$	11.1606	−	1.41184i	0.560843	−	0.0709477i
$397$	−10.3966	+	12.6683i	−0.521789	+	0.635802i	−0.965511	−	0.260363i	$-0.916158\pi$
$397$	−10.3966	+	12.6683i	−0.521789	+	0.635802i	0.443722	+	0.896164i	$0.353658\pi$
$398$	1.03452	−	1.06354i	0.0518558	−	0.0533102i
$399$	−7.44277	−	3.08290i	−0.372605	−	0.154338i
$400$	10.8896	+	14.4934i	0.544481	+	0.724668i
$401$	31.6820	−	13.1231i	1.58212	−	0.655337i	0.593375	−	0.804926i	$-0.297795\pi$
$401$	31.6820	−	13.1231i	1.58212	−	0.655337i	0.988748	+	0.149590i	$0.0477953\pi$
$402$	3.11728	−	7.83034i	0.155476	−	0.390542i
$403$	5.23138	−	0.515246i	0.260594	−	0.0256662i
$404$	−28.0435	+	9.36130i	−1.39521	+	0.465742i
$405$	0.603252	+	0.322445i	0.0299758	+	0.0160224i
$406$	−9.68086	−	17.5243i	−0.480453	−	0.869716i
$407$	5.71331	−	1.13645i	0.283198	−	0.0563317i
$408$	−0.544470	+	9.59459i	−0.0269553	+	0.475003i
$409$	2.02215	−	10.1660i	0.0999888	−	0.502678i	−0.898040	−	0.439915i	$-0.855009\pi$
$409$	2.02215	−	10.1660i	0.0999888	−	0.502678i	0.998028	−	0.0627632i	$-0.0199913\pi$
$410$	−2.12048	+	4.10261i	−0.104723	+	0.202614i
$411$	5.71773	+	0.563147i	0.282035	+	0.0277780i
$412$	6.06799	+	26.6336i	0.298948	+	1.31214i
$413$	−17.6038	−	5.34005i	−0.866226	−	0.262767i
$414$	13.0512	+	2.40891i	0.641430	+	0.118392i
$415$	−7.17396	−	7.17396i	−0.352156	−	0.352156i
$416$	17.3464	−	6.60204i	0.850478	−	0.323692i
$417$	15.4297	−	15.4297i	0.755594	−	0.755594i
$418$	−32.5125	+	22.3806i	−1.59024	+	1.09467i
$419$	8.89589	−	29.3258i	0.434593	−	1.43266i	−0.417216	−	0.908807i	$-0.636994\pi$
$419$	8.89589	−	29.3258i	0.434593	−	1.43266i	0.851809	−	0.523853i	$-0.175506\pi$
$420$	1.81192	−	1.28456i	0.0884127	−	0.0626802i
$421$	0.995282	−	10.1053i	0.0485071	−	0.492501i	−0.939984	−	0.341219i	$-0.889160\pi$
$421$	0.995282	−	10.1053i	0.0485071	−	0.492501i	0.988491	−	0.151281i	$-0.0483399\pi$
$422$	2.73547	−	0.871285i	0.133161	−	0.0424135i
$423$	4.07668	+	0.810902i	0.198215	+	0.0394274i
$424$	−21.4574	−	16.1681i	−1.04206	−	0.785191i
$425$	3.00412	+	15.1027i	0.145721	+	0.732589i
$426$	−12.7640	−	3.67994i	−0.618417	−	0.178294i
$427$	−3.52095	+	6.58723i	−0.170391	+	0.318778i
$428$	27.0404	+	1.90995i	1.30705	+	0.0923209i
$429$	−1.80892	−	18.3662i	−0.0873354	−	0.886731i
$430$	5.11998	−	2.20420i	0.246907	−	0.106296i
$431$	−14.3481	−	34.6395i	−0.691125	−	1.66852i	−0.742501	−	0.669844i	$-0.766361\pi$
$431$	−14.3481	−	34.6395i	−0.691125	−	1.66852i	0.0513763	−	0.998679i	$-0.483639\pi$
$432$	−2.94701	+	2.70465i	−0.141788	+	0.130127i
$433$	−9.82015	+	23.7079i	−0.471926	+	1.13933i	0.491385	+	0.870943i	$0.336491\pi$
$433$	−9.82015	+	23.7079i	−0.471926	+	1.13933i	−0.963311	+	0.268388i	$0.913509\pi$
$434$	0.0508707	+	3.67823i	0.00244187	+	0.176561i
$435$	−4.61052	−	3.78376i	−0.221058	−	0.181417i
$436$	−16.4214	+	9.37028i	−0.786441	+	0.448755i
$437$	−44.5604	+	13.5173i	−2.13161	+	0.646618i
$438$	−11.9356	+	1.34245i	−0.570303	+	0.0641448i
$439$	24.9003	+	16.6378i	1.18843	+	0.794081i	0.982822	−	0.184555i	$-0.0590843\pi$
$439$	24.9003	+	16.6378i	1.18843	+	0.794081i	0.205603	+	0.978635i	$0.434084\pi$
$440$	−0.451354	−	10.8729i	−0.0215175	−	0.518346i
$441$	−2.42457	−	3.62862i	−0.115456	−	0.172792i
$442$	15.7094	+	1.32816i	0.747218	+	0.0631743i
$443$	8.66514	+	10.5585i	0.411693	+	0.501649i	0.937032	−	0.349244i	$-0.113561\pi$
$443$	8.66514	+	10.5585i	0.411693	+	0.501649i	−0.525339	+	0.850893i	$0.676061\pi$
$444$	−1.42355	+	1.50456i	−0.0675586	+	0.0714031i
$445$	3.13273	−	1.67448i	0.148505	−	0.0793778i
$446$	−11.7886	−	7.64319i	−0.558204	−	0.361915i
$447$		−	6.00928i		−	0.284229i
$448$	3.58098	+	12.4849i	0.169185	+	0.589858i
$449$			19.2189i			0.906998i	0.891257	+	0.453499i	$0.149824\pi$
$449$			19.2189i			0.906998i	−0.891257	+	0.453499i	$0.850176\pi$
$450$	−3.48682	+	5.37794i	−0.164370	+	0.253518i
$451$	−23.6824	+	12.6585i	−1.11516	+	0.596066i
$452$	−25.2439	+	0.698390i	−1.18737	+	0.0328495i
$453$	2.44361	+	2.97755i	0.114811	+	0.139897i
$454$	2.14032	−	25.3154i	0.100450	−	1.18811i
$455$	−2.02433	−	3.02963i	−0.0949021	−	0.142031i
$456$	4.82840	−	13.1779i	0.226111	−	0.617111i
$457$	15.7178	+	10.5023i	0.735250	+	0.491278i	0.865942	−	0.500145i	$-0.166720\pi$
$457$	15.7178	+	10.5023i	0.735250	+	0.491278i	−0.130692	+	0.991423i	$0.541720\pi$
$458$	0.295610	+	2.62823i	0.0138129	+	0.122809i
$459$	−3.25136	+	0.986288i	−0.151760	+	0.0460360i
$460$	3.38558	−	12.3839i	0.157854	−	0.577400i
$461$	−29.2557	−	24.0095i	−1.36257	−	1.11823i	−0.981024	−	0.193884i	$-0.937891\pi$
$461$	−29.2557	−	24.0095i	−1.36257	−	1.11823i	−0.381547	−	0.924349i	$-0.624609\pi$
$462$	12.9135	−	0.178596i	0.600790	−	0.00830905i
$463$	−13.7419	+	33.1759i	−0.638640	+	1.54181i	0.189852	+	0.981813i	$0.439199\pi$
$463$	−13.7419	+	33.1759i	−0.638640	+	1.54181i	−0.828492	+	0.560001i	$0.810801\pi$
$464$	29.8039	−	18.1171i	1.38361	−	0.841064i
$465$	0.419383	+	1.01248i	0.0194484	+	0.0469526i
$466$	−3.20192	−	7.43752i	−0.148326	−	0.344536i
$467$	1.34775	+	13.6840i	0.0623665	+	0.633218i	0.974662	+	0.223684i	$0.0718085\pi$
$467$	1.34775	+	13.6840i	0.0623665	+	0.633218i	−0.912295	+	0.409533i	$0.865691\pi$
$468$	4.30162	+	4.95548i	0.198842	+	0.229067i
$469$	4.56101	−	8.53305i	0.210608	−	0.394020i
$470$	1.11387	−	3.86347i	0.0513788	−	0.178209i
$471$	3.48057	+	17.4980i	0.160376	+	0.806266i
$472$	8.02308	−	31.0276i	0.369292	−	1.42816i
$473$	31.7897	+	6.32336i	1.46169	+	0.290748i
$474$	−2.42361	−	7.60912i	−0.111320	−	0.349499i
$475$	2.20424	−	22.3800i	0.101137	−	1.02687i
$476$	−1.85227	+	10.8759i	−0.0848985	+	0.498495i
$477$	2.75737	−	9.08984i	0.126251	−	0.416195i
$478$	4.29804	+	6.24379i	0.196588	+	0.285584i
$479$	−0.0933241	+	0.0933241i	−0.00426409	+	0.00426409i	−0.709236	−	0.704972i	$-0.750960\pi$
$479$	−0.0933241	+	0.0933241i	−0.00426409	+	0.00426409i	0.704972	+	0.709236i	$0.250960\pi$
$480$	2.36687	+	3.06107i	0.108033	+	0.139718i
$481$	2.40272	+	2.40272i	0.109555	+	0.109555i
$482$	−7.28894	+	39.4905i	−0.332002	+	1.79874i
$483$	14.5800	+	4.42280i	0.663413	+	0.201244i
$484$	21.9741	−	34.9413i	0.998824	−	1.58824i
$485$	2.20795	+	0.217464i	0.100258	+	0.00987453i
$486$	−1.25632	−	0.649344i	−0.0569881	−	0.0294549i
$487$	−3.94499	+	19.8328i	−0.178765	+	0.898710i	0.782409	+	0.622765i	$0.213991\pi$
$487$	−3.94499	+	19.8328i	−0.178765	+	0.898710i	−0.961173	+	0.275945i	$0.911009\pi$
$488$	−11.7204	−	5.65271i	−0.530556	−	0.255886i
$489$	−4.81554	+	0.957870i	−0.217766	+	0.0433164i
$490$	−3.69526	+	2.04135i	−0.166935	+	0.0922190i
$491$	−7.76577	−	4.15089i	−0.350464	−	0.187327i	0.286766	−	0.958001i	$-0.407420\pi$
$491$	−7.76577	−	4.15089i	−0.350464	−	0.187327i	−0.637230	+	0.770674i	$0.719920\pi$
$492$	4.26637	−	8.54198i	0.192343	−	0.385102i
$493$	29.4835	−	2.90387i	1.32787	−	0.130784i
$494$	−21.3912	−	8.51590i	−0.962436	−	0.383149i
$495$	3.55460	−	1.47236i	0.159767	−	0.0661778i
$496$	−6.39878	+	0.354325i	−0.287314	+	0.0159096i
$497$	−14.0893	−	5.83597i	−0.631991	−	0.261779i
$498$	15.0359	+	14.6257i	0.673774	+	0.655391i
$499$	−1.48788	+	1.81299i	−0.0666067	+	0.0811605i	−0.805248	−	0.592938i	$-0.797968\pi$
$499$	−1.48788	+	1.81299i	−0.0666067	+	0.0811605i	0.738641	+	0.674099i	$0.235468\pi$
$500$	10.3052	+	7.99075i	0.460864	+	0.357357i
$501$	3.86728	+	12.7487i	0.172777	+	0.569570i
$502$	−4.72242	−	3.76752i	−0.210772	−	0.168152i
$503$	−14.7895	+	22.1341i	−0.659433	+	0.986911i	0.339495	+	0.940608i	$0.389744\pi$
$503$	−14.7895	+	22.1341i	−0.659433	+	0.986911i	−0.998927	+	0.0463028i	$0.985256\pi$
$504$	−3.70907	+	2.70739i	−0.165215	+	0.120597i
$505$	−8.40733	+	5.61760i	−0.374121	+	0.249980i
$506$	57.0449	−	48.1510i	2.53596	−	2.14057i
$507$	−1.72755	+	1.41776i	−0.0767232	+	0.0629651i
$508$	−16.8493	+	7.53167i	−0.747567	+	0.334164i
$509$	1.75243	+	3.27856i	0.0776750	+	0.145320i	0.917761	−	0.397134i	$-0.129995\pi$
$509$	1.75243	+	3.27856i	0.0776750	+	0.145320i	−0.840086	+	0.542454i	$0.817495\pi$
$510$	0.685725	+	3.21440i	0.0303644	+	0.142336i
$511$	−13.7886			−0.609974
$512$	−21.4729	+	7.13530i	−0.948979	+	0.315339i
$513$	4.96199			0.219077
$514$	0.621815	+	2.91481i	0.0274271	+	0.128567i
$515$	4.40397	+	8.23925i	0.194062	+	0.363065i
$516$	−10.5215	+	4.70314i	−0.463185	+	0.207044i
$517$	18.0728	−	14.8319i	0.794839	−	0.652307i
$518$	−1.81707	+	1.53377i	−0.0798377	+	0.0673901i
$519$	8.59408	−	5.74238i	0.377238	−	0.252062i
$520$	5.12720	−	3.74253i	0.224843	−	0.164121i
$521$	2.03873	−	3.05118i	0.0893184	−	0.133674i	−0.784120	−	0.620610i	$-0.786885\pi$
$521$	2.03873	−	3.05118i	0.0893184	−	0.133674i	0.873438	+	0.486935i	$0.161885\pi$
$522$	9.63954	+	7.69036i	0.421911	+	0.336598i
$523$	−4.37005	−	14.4061i	−0.191089	−	0.629935i	−0.999165	−	0.0408573i	$-0.986991\pi$
$523$	−4.37005	−	14.4061i	−0.191089	−	0.629935i	0.808076	−	0.589078i	$-0.200509\pi$
$524$	−1.29575	−	1.00474i	−0.0566051	−	0.0438921i
$525$	−4.66792	+	5.68788i	−0.203725	+	0.248239i
$526$	9.67884	+	9.41478i	0.422018	+	0.410504i
$527$	−5.02918	−	2.08315i	−0.219074	−	0.0907436i
$528$	1.24396	+	22.4647i	0.0541363	+	0.977653i
$529$	60.1150	−	24.9005i	2.61370	−	1.08263i
$530$	−8.53708	−	3.39864i	−0.370827	−	0.147627i
$531$	11.2762	−	1.11061i	0.489344	−	0.0481962i
$532$	7.19927	−	14.4141i	0.312128	−	0.624931i
$533$	−13.8143	−	7.38392i	−0.598365	−	0.319833i
$534$	−6.42843	+	3.55122i	−0.278185	+	0.153676i
$535$	9.09298	−	1.80871i	0.393124	−	0.0781972i
$536$	15.1825	+	7.32248i	0.655783	+	0.316283i
$537$	−4.71609	+	23.7094i	−0.203514	+	1.02314i
$538$	−11.2414	−	5.81026i	−0.484653	−	0.250498i
$539$	−24.4290	−	2.40605i	−1.05223	−	0.103636i
$540$	−0.728294	+	1.15807i	−0.0313408	+	0.0498353i
$541$	−22.3890	−	6.79163i	−0.962578	−	0.291995i	−0.230391	−	0.973098i	$-0.574000\pi$
$541$	−22.3890	−	6.79163i	−0.962578	−	0.291995i	−0.732187	+	0.681103i	$0.761500\pi$
$542$	−4.62708	+	25.0689i	−0.198750	+	1.07680i
$543$	3.53760	+	3.53760i	0.151813	+	0.151813i
$544$	−19.0648	−	2.43826i	−0.817395	−	0.104540i
$545$	−4.57235	+	4.57235i	−0.195858	+	0.195858i
$546$	4.27154	+	6.20529i	0.182805	+	0.265562i
$547$	11.8981	−	39.2227i	0.508725	−	1.67704i	−0.206744	−	0.978395i	$-0.566287\pi$
$547$	11.8981	−	39.2227i	0.508725	−	1.67704i	0.715468	−	0.698645i	$-0.246213\pi$
$548$	−1.92921	+	11.3277i	−0.0824118	+	0.483895i
$549$	0.450932	−	4.57839i	0.0192453	−	0.195401i
$550$	10.9413	+	34.3510i	0.466537	+	1.46473i
$551$	−42.4351	−	8.44087i	−1.80780	−	0.359593i
$552$	−6.64496	+	25.6980i	−0.282828	+	1.09378i
$553$	−1.78855	−	8.99166i	−0.0760570	−	0.382364i
$554$	−11.8460	+	41.0881i	−0.503287	+	1.74566i
$555$	−0.333936	+	0.624750i	−0.0141748	+	0.0265191i
$556$	28.6083	+	32.9569i	1.21326	+	1.39768i
$557$	3.23277	+	32.8228i	0.136977	+	1.39075i	0.780421	+	0.625255i	$0.215005\pi$
$557$	3.23277	+	32.8228i	0.136977	+	1.39075i	−0.643444	+	0.765493i	$0.722495\pi$
$558$	−0.895940	−	2.08111i	−0.0379282	−	0.0881006i
$559$	7.23528	+	17.4675i	0.306020	+	0.738797i
$560$	2.30741	+	3.79585i	0.0975059	+	0.160404i
$561$	−7.31351	+	17.6564i	−0.308777	+	0.745453i
$562$	−7.68593	+	0.106298i	−0.324211	+	0.00448391i
$563$	11.5252	+	9.45849i	0.485729	+	0.398628i	0.845134	−	0.534554i	$-0.179520\pi$
$563$	11.5252	+	9.45849i	0.485729	+	0.398628i	−0.359405	+	0.933182i	$0.617020\pi$
$564$	−2.19224	+	8.01883i	−0.0923100	+	0.337654i
$565$	−8.26506	+	2.50718i	−0.347714	+	0.105478i
$566$	0.154793	+	1.37625i	0.00650643	+	0.0578479i
$567$	−1.34993	−	0.901992i	−0.0566916	−	0.0378801i
$568$	9.14024	−	24.9460i	0.383516	−	1.04671i
$569$	16.1927	+	24.2342i	0.678835	+	1.01595i	0.997676	+	0.0681404i	$0.0217066\pi$
$569$	16.1927	+	24.2342i	0.678835	+	1.01595i	−0.318840	+	0.947808i	$0.603293\pi$
$570$	0.404376	−	4.78291i	0.0169375	−	0.200334i
$571$	−19.4336	−	23.6799i	−0.813271	−	0.990974i	−0.999963	−	0.00855545i	$-0.997277\pi$
$571$	−19.4336	−	23.6799i	−0.813271	−	0.990974i	0.186692	−	0.982418i	$-0.440223\pi$
$572$	36.8961	−	1.02076i	1.54270	−	0.0426800i
$573$	14.0291	−	7.49872i	0.586075	−	0.313264i
$574$	5.96324	−	9.19747i	0.248901	−	0.383895i
$575$			42.5315i			1.77368i
$576$	−4.98057	−	6.26050i	−0.207524	−	0.260854i
$577$			35.4216i			1.47462i	0.675554	+	0.737311i	$0.263905\pi$
$577$			35.4216i			1.47462i	−0.675554	+	0.737311i	$0.736095\pi$
$578$	6.47414	+	4.19756i	0.269289	+	0.174595i
$579$	5.30117	−	2.83353i	0.220309	−	0.117758i
$580$	8.19840	−	8.66494i	0.340420	−	0.359792i
$581$	15.2766	+	18.6146i	0.633781	+	0.772265i
$582$	−4.57073	−	0.386437i	−0.189463	−	0.0160183i
$583$	−29.6836	−	44.4246i	−1.22937	−	1.83988i
$584$	−0.996323	−	24.0010i	−0.0412281	−	0.993167i
$585$	1.86606	+	1.24686i	0.0771521	+	0.0515514i
$586$	1.65739	−	0.186415i	0.0684662	−	0.00770073i
$587$	5.22336	−	1.58449i	0.215591	−	0.0653989i	−0.180641	−	0.983549i	$-0.557817\pi$
$587$	5.22336	−	1.58449i	0.215591	−	0.0653989i	0.396233	+	0.918150i	$0.370317\pi$
$588$	7.58087	−	4.32576i	0.312630	−	0.178391i
$589$	6.14530	+	5.04331i	0.253213	+	0.207806i
$590$	−0.151575	−	10.9597i	−0.00624025	−	0.451205i
$591$	2.73473	−	6.60221i	0.112492	−	0.271579i
$592$	−2.80103	−	3.05203i	−0.115122	−	0.125438i
$593$	−7.79302	−	18.8140i	−0.320021	−	0.772599i	−0.999252	−	0.0386746i	$-0.987686\pi$
$593$	−7.79302	−	18.8140i	−0.320021	−	0.772599i	0.679231	−	0.733925i	$-0.262314\pi$
$594$	−7.30634	+	3.14545i	−0.299783	+	0.129060i
$595$	0.369840	+	3.75505i	0.0151620	+	0.153942i
$596$	11.9887	+	0.846801i	0.491076	+	0.0346863i
$597$	−0.494555	+	0.925248i	−0.0202408	+	0.0378679i
$598$	41.8404	+	12.0629i	1.71098	+	0.493288i
$599$	4.00059	+	20.1123i	0.163460	+	0.821767i	0.972300	+	0.233738i	$0.0750959\pi$
$599$	4.00059	+	20.1123i	0.163460	+	0.821767i	−0.808840	+	0.588029i	$0.799904\pi$
$600$	−10.2378	−	7.71415i	−0.417956	−	0.314929i
$601$	−14.0359	−	2.79192i	−0.572537	−	0.113885i	−0.0996730	−	0.995020i	$-0.531780\pi$
$601$	−14.0359	−	2.79192i	−0.572537	−	0.113885i	−0.472864	+	0.881136i	$0.656780\pi$
$602$	−12.6067	+	4.01540i	−0.513811	+	0.163656i
$603$	−0.584134	+	5.93082i	−0.0237878	+	0.241521i
$604$	−6.28464	+	4.45549i	−0.255718	+	0.181291i
$605$	4.09795	−	13.5091i	0.166605	−	0.549224i
$606$	17.2199	−	11.8537i	0.699511	−	0.481523i
$607$	25.3564	−	25.3564i	1.02919	−	1.02919i	0.0296246	−	0.999561i	$-0.490569\pi$
$607$	25.3564	−	25.3564i	1.02919	−	1.02919i	0.999561	−	0.0296246i	$-0.00943119\pi$
$608$	25.6099	+	11.4898i	1.03862	+	0.465972i
$609$	10.0102	+	10.0102i	0.405636	+	0.405636i
$610$	−4.37641	−	0.807774i	−0.177196	−	0.0327058i
$611$	13.0505	+	3.95883i	0.527968	+	0.160157i
$612$	−1.50951	−	6.62554i	−0.0610182	−	0.267821i
$613$	−1.89369	−	0.186512i	−0.0764853	−	0.00753314i	0.0597021	−	0.998216i	$-0.480985\pi$
$613$	−1.89369	−	0.186512i	−0.0764853	−	0.00753314i	−0.136187	+	0.990683i	$0.543485\pi$
$614$	−2.42055	+	4.68318i	−0.0976853	+	0.188998i
$615$	0.637080	−	3.20282i	0.0256896	−	0.129150i
$616$	−1.46341	+	25.7880i	−0.0589623	+	1.03903i
$617$	−0.396030	+	0.0787753i	−0.0159436	+	0.00317137i	−0.203056	−	0.979167i	$-0.565087\pi$
$617$	−0.396030	+	0.0787753i	−0.0159436	+	0.00317137i	0.187112	+	0.982339i	$0.440087\pi$
$618$	−9.33992	−	16.9071i	−0.375707	−	0.680105i
$619$	−14.3068	−	7.64714i	−0.575038	−	0.307364i	0.158123	−	0.987419i	$-0.449456\pi$
$619$	−14.3068	−	7.64714i	−0.575038	−	0.307364i	−0.733161	+	0.680055i	$0.761956\pi$
$620$	−2.07902	+	0.694007i	−0.0834956	+	0.0278720i
$621$	−9.33927	+	0.919838i	−0.374772	+	0.0369118i
$622$	−1.19034	+	2.99002i	−0.0477281	+	0.119889i
$623$	−7.78938	+	3.22647i	−0.312075	+	0.129266i
$624$	−10.4925	+	7.88355i	−0.420036	+	0.315595i
$625$	−16.8152	−	6.96509i	−0.672609	−	0.278604i
$626$	6.61243	−	6.79790i	0.264286	−	0.271699i
$627$	17.7060	−	21.5748i	0.707109	−	0.861615i
$628$	−35.3995	+	4.47810i	−1.41260	+	0.178696i
$629$	−1.02144	−	3.36723i	−0.0407273	−	0.134260i
$630$	−0.979452	+	1.22770i	−0.0390223	+	0.0489128i
$631$	−3.64605	+	5.45670i	−0.145147	+	0.217228i	−0.896918	−	0.442196i	$-0.854200\pi$
$631$	−3.64605	+	5.45670i	−0.145147	+	0.217228i	0.751772	+	0.659424i	$0.229200\pi$
$632$	15.5219	−	3.76292i	0.617430	−	0.149681i
$633$	−1.68790	+	1.12782i	−0.0670880	+	0.0448268i
$634$	10.8587	+	12.8644i	0.431253	+	0.510909i
$635$	−4.87935	+	4.00438i	−0.193631	+	0.158909i
$636$	17.7459	+	6.78194i	0.703672	+	0.268921i
$637$	−6.74982	−	12.6280i	−0.267438	−	0.500341i
$638$	67.8349	−	14.4712i	2.68561	−	0.572920i
$639$	9.39312			0.371586
$640$	−6.44046	+	4.29063i	−0.254582	+	0.169602i
$641$	14.4288			0.569902			0.284951	−	0.958542i	$-0.408023\pi$
$641$	14.4288			0.569902			0.284951	+	0.958542i	$0.408023\pi$
$642$	−18.7463	+	3.99913i	−0.739856	+	0.157833i
$643$	0.357566	+	0.668959i	0.0141010	+	0.0263812i	0.888873	−	0.458153i	$-0.151489\pi$
$643$	0.357566	+	0.668959i	0.0141010	+	0.0263812i	−0.874772	+	0.484535i	$0.838989\pi$
$644$	−10.8782	+	28.4643i	−0.428659	+	1.12165i
$645$	−3.04691	+	2.50053i	−0.119972	+	0.0984584i
$646$	15.3789	+	18.2195i	0.605074	+	0.716837i
$647$	24.1171	−	16.1145i	0.948142	−	0.633528i	0.0176513	−	0.999844i	$-0.494381\pi$
$647$	24.1171	−	16.1145i	0.948142	−	0.633528i	0.930490	+	0.366316i	$0.119381\pi$
$648$	1.47250	−	2.41490i	0.0578451	−	0.0948663i
$649$	35.4081	−	52.9920i	1.38989	−	2.08012i
$650$	−13.1148	+	16.4389i	−0.514406	+	0.644785i
$651$	−0.755075	−	2.48915i	−0.0295937	−	0.0975574i
$652$	−1.23240	−	9.74212i	−0.0482643	−	0.381531i
$653$	−2.22203	+	2.70755i	−0.0869546	+	0.105955i	−0.814670	−	0.579924i	$-0.803082\pi$
$653$	−2.22203	+	2.70755i	−0.0869546	+	0.105955i	0.727716	+	0.685879i	$0.240582\pi$
$654$	9.32172	−	9.58318i	0.364508	−	0.374732i
$655$	−0.518091	−	0.214600i	−0.0202435	−	0.00838513i
$656$	16.4403	+	9.71524i	0.641886	+	0.379316i
$657$	7.84645	−	3.25010i	0.306119	−	0.126799i
$658$	−3.52989	+	8.86678i	−0.137609	+	0.345663i
$659$	−20.9913	+	2.06747i	−0.817707	+	0.0805371i	−0.498217	−	0.867053i	$-0.666012\pi$
$659$	−20.9913	+	2.06747i	−0.817707	+	0.0805371i	−0.319490	+	0.947590i	$0.603512\pi$
$660$	2.43651	+	7.29901i	0.0948410	+	0.284113i
$661$	−27.2996	−	14.5919i	−1.06183	−	0.567561i	−0.154507	−	0.987992i	$-0.549379\pi$
$661$	−27.2996	−	14.5919i	−1.06183	−	0.567561i	−0.907325	+	0.420431i	$0.861879\pi$
$662$	−6.53763	−	11.8344i	−0.254092	−	0.459958i
$663$	−10.9336	+	2.17483i	−0.424627	+	0.0844635i
$664$	−31.2974	+	27.9360i	−1.21457	+	1.08413i
$665$	1.07504	−	5.40458i	0.0416882	−	0.209581i
$666$	0.672485	−	1.30110i	0.0260583	−	0.0504165i
$667$	81.4346	+	8.02061i	3.15316	+	0.310559i
$668$	−25.9790	+	5.91884i	−1.00516	+	0.229007i
$669$	9.50672	+	2.88383i	0.367551	+	0.111495i
$670$	5.66918	+	1.04638i	0.219019	+	0.0404254i
$671$	−18.2979	−	18.2979i	−0.706382	−	0.706382i
$672$	−4.87865	−	7.78121i	−0.188198	−	0.300167i
$673$	−19.3713	+	19.3713i	−0.746710	+	0.746710i	−0.973860	−	0.227150i	$-0.927059\pi$
$673$	−19.3713	+	19.3713i	−0.746710	+	0.746710i	0.227150	+	0.973860i	$0.427059\pi$
$674$	−4.15710	+	2.86162i	−0.160126	+	0.110226i
$675$	1.31560	−	4.33697i	0.0506376	−	0.166930i
$676$	−2.58504	−	3.64630i	−0.0994247	−	0.140242i
$677$	4.67558	−	47.4719i	0.179697	−	1.82449i	−0.307892	−	0.951421i	$-0.599623\pi$
$677$	4.67558	−	47.4719i	0.179697	−	1.82449i	0.487589	−	0.873073i	$-0.337877\pi$
$678$	17.0147	−	5.41942i	0.653447	−	0.208131i
$679$	−5.16481	−	1.02734i	−0.198207	−	0.0394259i
$680$	−6.50944	+	0.915084i	−0.249626	+	0.0350919i
$681$	3.50471	+	17.6194i	0.134301	+	0.675176i
$682$	−12.2457	−	3.53053i	−0.468914	−	0.135191i
$683$	12.5319	−	23.4455i	0.479518	−	0.897116i	−0.519570	−	0.854428i	$-0.673908\pi$
$683$	12.5319	−	23.4455i	0.479518	−	0.897116i	0.999088	−	0.0426879i	$-0.0135921\pi$
$684$	−0.699220	+	9.89931i	−0.0267354	+	0.378509i
$685$	0.385204	+	3.91104i	0.0147179	+	0.149433i
$686$	23.9659	−	10.3175i	0.915020	−	0.393925i
$687$	−0.715679	−	1.72780i	−0.0273048	−	0.0659197i
$688$	−7.90027	−	21.6535i	−0.301195	−	0.825533i
$689$	11.9267	−	28.7937i	0.454372	−	1.09695i
$690$	0.125539	+	9.07719i	0.00477920	+	0.345563i
$691$	−15.6483	−	12.8422i	−0.595290	−	0.488542i	0.287835	−	0.957680i	$-0.407065\pi$
$691$	−15.6483	−	12.8422i	−0.595290	−	0.488542i	−0.883125	+	0.469138i	$0.844565\pi$
$692$	10.2452	+	17.9546i	0.389463	+	0.682532i
$693$	−8.73886	+	2.65091i	−0.331962	+	0.100700i
$694$	40.2269	−	4.52452i	1.52699	−	0.171748i
$695$	12.4104	+	8.29237i	0.470754	+	0.314548i
$696$	−16.7009	+	18.1475i	−0.633045	+	0.687878i
$697$	9.01174	+	13.4870i	0.341344	+	0.510857i
$698$	−8.37168	−	0.707793i	−0.316873	−	0.0267903i
$699$	3.63239	+	4.42608i	0.137390	+	0.167410i
$700$	−10.6897	−	10.1141i	−0.404033	−	0.382279i
$701$	−40.6074	+	21.7051i	−1.53372	+	0.819791i	−0.999671	−	0.0256614i	$-0.991831\pi$
$701$	−40.6074	+	21.7051i	−1.53372	+	0.819791i	−0.534051	+	0.845453i	$0.679331\pi$
$702$	−3.89336	−	2.52429i	−0.146946	−	0.0952732i
$703$			5.13882i			0.193814i
$704$	−44.9931	−	0.683897i	−1.69574	−	0.0257753i
$705$			2.84316i			0.107080i
$706$	20.7331	−	31.9780i	0.780302	−	1.20351i
$707$	21.1659	−	11.3134i	0.796026	−	0.425485i
$708$	0.626705	+	22.6528i	0.0235530	+	0.851344i
$709$	9.19792	+	11.2077i	0.345435	+	0.420914i	0.916527	−	0.399972i	$-0.130980\pi$
$709$	9.19792	+	11.2077i	0.345435	+	0.420914i	−0.571092	+	0.820886i	$0.693480\pi$
$710$	0.765491	−	9.05413i	0.0287284	−	0.339795i
$711$	3.13719	+	4.69514i	0.117654	+	0.176081i
$712$	−6.17893	−	13.3253i	−0.231565	−	0.499388i
$713$	−12.5014	−	8.35315i	−0.468180	−	0.312828i
$714$	−0.871935	−	7.75227i	−0.0326313	−	0.290121i
$715$	12.0801	−	3.66446i	0.451770	−	0.137043i
$716$	−46.6364	−	12.7498i	−1.74288	−	0.476481i
$717$	−4.14329	−	3.40031i	−0.154734	−	0.126987i
$718$	−17.0846	+	0.236284i	−0.637592	+	0.00881803i
$719$	2.99840	−	7.23877i	0.111821	−	0.269961i	−0.858055	−	0.513557i	$-0.828327\pi$
$719$	2.99840	−	7.23877i	0.111821	−	0.269961i	0.969877	+	0.243597i	$0.0783274\pi$
$720$	−2.20775	−	1.61616i	−0.0822780	−	0.0602306i
$721$	−8.48579	−	20.4865i	−0.316027	−	0.762958i
$722$	−3.14350	−	7.30180i	−0.116989	−	0.271745i
$723$	−2.78327	−	28.2590i	−0.103511	−	1.05096i
$724$	−7.55612	+	6.55911i	−0.280821	+	0.243767i
$725$	−18.6287	+	34.8519i	−0.691854	+	1.29437i
$726$	−8.08547	+	28.0446i	−0.300080	+	1.04083i
$727$	−5.73325	−	28.8230i	−0.212635	−	1.06899i	−0.928666	−	0.370918i	$-0.879043\pi$
$727$	−5.73325	−	28.8230i	−0.212635	−	1.06899i	0.716031	−	0.698068i	$-0.245957\pi$
$728$	−12.9817	+	7.64742i	−0.481132	+	0.283432i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	−2.49337	−	7.82814i	−0.0922837	−	0.289733i
$731$	1.91905	−	19.4845i	0.0709788	−	0.720660i
$732$	9.07048	+	1.54479i	0.335255	+	0.0570970i
$733$	−5.22978	+	17.2403i	−0.193166	+	0.636784i	0.805837	+	0.592138i	$0.201716\pi$
$733$	−5.22978	+	17.2403i	−0.193166	+	0.636784i	−0.999003	+	0.0446458i	$0.985784\pi$
$734$	22.0536	+	32.0374i	0.814014	+	1.18252i
$735$	2.11081	−	2.11081i	0.0778584	−	0.0778584i
$736$	−50.3319	−	16.8781i	−1.85526	−	0.622137i
$737$	23.7029	+	23.7029i	0.873109	+	0.873109i
$738$	−1.22547	+	6.63942i	−0.0451101	+	0.244401i
$739$	−19.6837	−	5.97099i	−0.724077	−	0.219646i	−0.0933304	−	0.995635i	$-0.529751\pi$
$739$	−19.6837	−	5.97099i	−0.724077	−	0.219646i	−0.630747	+	0.775989i	$0.717251\pi$
$740$	−1.19934	−	0.754248i	−0.0440885	−	0.0277267i
$741$	16.2020	+	1.59576i	0.595197	+	0.0586217i
$742$	19.3748	+	10.0141i	0.711271	+	0.367627i
$743$	1.47610	−	7.42086i	0.0541529	−	0.272245i	−0.944217	−	0.329325i	$-0.893179\pi$
$743$	1.47610	−	7.42086i	0.0541529	−	0.272245i	0.998370	+	0.0570798i	$0.0181789\pi$
$744$	4.27813	−	1.49417i	0.156844	−	0.0547788i
$745$	4.03149	−	0.801913i	0.147702	−	0.0293798i
$746$	−1.74219	+	0.962429i	−0.0637861	+	0.0352370i
$747$	−13.0808	−	6.99184i	−0.478602	−	0.255818i
$748$	−34.1944	−	17.0787i	−1.25027	−	0.624460i
$749$	−21.8993	+	2.15690i	−0.800184	+	0.0788113i
$750$	−8.56698	−	3.41054i	−0.312822	−	0.124535i
$751$	20.2044	−	8.36892i	0.737267	−	0.305386i	0.0177327	−	0.999843i	$-0.494355\pi$
$751$	20.2044	−	8.36892i	0.737267	−	0.305386i	0.719535	+	0.694457i	$0.244355\pi$
$752$	−15.6889	−	5.50356i	−0.572114	−	0.200694i
$753$	3.94657	+	1.63472i	0.143821	+	0.0595726i
$754$	29.0021	+	28.2109i	1.05620	+	1.02738i
$755$	−1.67148	+	2.03670i	−0.0608313	+	0.0741232i
$756$	1.98973	−	2.56604i	0.0723656	−	0.0933259i
$757$	−2.62194	−	8.64338i	−0.0952961	−	0.314149i	0.896313	−	0.443422i	$-0.146236\pi$
$757$	−2.62194	−	8.64338i	−0.0952961	−	0.314149i	−0.991609	+	0.129273i	$0.958736\pi$
$758$	−33.9007	−	27.0457i	−1.23133	−	0.982345i
$759$	−29.3261	+	43.8896i	−1.06447	+	1.59309i
$760$	9.48507	+	1.48073i	0.344060	+	0.0537117i
$761$	−7.48021	+	4.99811i	−0.271157	+	0.181181i	−0.683713	−	0.729751i	$-0.739636\pi$
$761$	−7.48021	+	4.99811i	−0.271157	+	0.181181i	0.412556	+	0.910932i	$0.364636\pi$
$762$	9.97263	−	8.41779i	0.361270	−	0.304944i
$763$	11.8641	−	9.73662i	0.429510	−	0.352489i
$764$	12.9832	+	29.0452i	0.469717	+	1.05082i
$765$	−1.09556	−	2.04964i	−0.0396099	−	0.0741050i
$766$	−2.55116	−	11.9588i	−0.0921773	−	0.432089i
$767$	37.1765			1.34236
$768$	13.1917	−	9.05419i	0.476015	−	0.326715i
$769$	5.14530			0.185544			0.0927722	−	0.995687i	$-0.470427\pi$
$769$	5.14530			0.185544			0.0927722	+	0.995687i	$0.470427\pi$
$770$	1.84306	+	8.63952i	0.0664194	+	0.311347i
$771$	−0.993450	−	1.85861i	−0.0357782	−	0.0669364i
$772$	4.90597	+	10.9753i	0.176570	+	0.395009i
$773$	−29.5479	+	24.2494i	−1.06277	+	0.872189i	−0.992117	−	0.125312i	$-0.960007\pi$
$773$	−29.5479	+	24.2494i	−1.06277	+	0.872189i	−0.0706481	+	0.997501i	$0.522507\pi$
$774$	6.22740	−	5.25648i	0.223839	−	0.188940i
$775$	6.03739	−	4.03406i	0.216870	−	0.144908i
$776$	1.41504	−	9.06428i	0.0507969	−	0.325389i
$777$	0.934136	−	1.39803i	0.0335120	−	0.0501542i
$778$	1.90855	+	1.52263i	0.0684248	+	0.0545889i
$779$	−6.87653	−	22.6689i	−0.246377	−	0.812197i
$780$	−2.75048	+	3.54714i	−0.0984830	+	0.127008i
$781$	33.5177	−	40.8415i	1.19936	−	1.46142i
$782$	−32.3231	−	31.4412i	−1.15587	−	1.12433i
$783$	−8.05585	−	3.33684i	−0.287893	−	0.119249i
$784$	7.56175	+	15.7336i	0.270063	+	0.561915i
$785$	−11.2745	+	4.67007i	−0.402406	+	0.166682i
$786$	1.07719	+	0.428832i	0.0384220	+	0.0152959i
$787$	−36.7644	+	3.62098i	−1.31051	+	0.129074i	−0.729027	−	0.684485i	$-0.760027\pi$
$787$	−36.7644	+	3.62098i	−1.31051	+	0.129074i	−0.581483	+	0.813559i	$0.697527\pi$
$788$	12.7862	+	6.38621i	0.455491	+	0.227499i
$789$	−8.42034	−	4.50077i	−0.299772	−	0.160232i
$790$	4.78136	−	2.64134i	0.170113	−	0.0939748i
$791$	20.1062	−	3.99938i	0.714895	−	0.142201i
$792$	−5.24570	−	15.0196i	−0.186398	−	0.533699i
$793$	2.94480	−	14.8045i	0.104573	−	0.525723i
$794$	20.5889	+	10.6416i	0.730673	+	0.377656i
$795$	6.46612	+	0.636857i	0.229330	+	0.0225870i
$796$	−1.77621	−	1.11703i	−0.0629560	−	0.0395922i
$797$	−7.14330	−	2.16690i	−0.253029	−	0.0767554i	0.161222	−	0.986918i	$-0.448456\pi$
$797$	−7.14330	−	2.16690i	−0.253029	−	0.0767554i	−0.414251	+	0.910163i	$0.635956\pi$
$798$	−2.06791	+	11.2037i	−0.0732031	+	0.396605i
$799$	−9.98613	−	9.98613i	−0.353284	−	0.353284i
$800$	16.8326	−	19.3377i	0.595123	−	0.683690i
$801$	3.67205	−	3.67205i	0.129746	−	0.129746i
$802$	−27.4984	−	39.9471i	−0.971001	−	1.41058i
$803$	13.8672	−	45.7140i	0.489362	−	1.61321i
$804$	−11.7498	−	2.00111i	−0.414385	−	0.0705737i
$805$	−1.02151	+	10.3716i	−0.0360036	+	0.365550i
$806$	−2.25617	−	7.08345i	−0.0794703	−	0.249504i
$807$	8.77595	+	1.74565i	0.308928	+	0.0614496i
$808$	21.2219	+	36.0246i	0.746583	+	1.26734i
$809$	1.18522	+	5.95853i	0.0416703	+	0.209491i	0.996011	−	0.0892293i	$-0.0284404\pi$
$809$	1.18522	+	5.95853i	0.0416703	+	0.209491i	−0.954341	+	0.298720i	$0.903440\pi$
$810$	0.267979	−	0.929491i	0.00941581	−	0.0326590i
$811$	−23.8921	+	44.6989i	−0.838964	+	1.56959i	−0.0171369	+	0.999853i	$0.505455\pi$
$811$	−23.8921	+	44.6989i	−0.838964	+	1.56959i	−0.821827	+	0.569737i	$0.807045\pi$
$812$	−21.3813	+	18.5601i	−0.750338	+	0.651333i
$813$	−1.76684	−	17.9390i	−0.0619658	−	0.629150i
$814$	−3.25755	−	7.56672i	−0.114177	−	0.265213i
$815$	−1.28523	−	3.10281i	−0.0450195	−	0.108687i
$816$	13.4309	−	2.07787i	0.470174	−	0.0727401i
$817$	−10.9421	+	26.4166i	−0.382816	+	0.924198i
$818$	−14.6572	+	0.202712i	−0.512477	+	0.00708766i
$819$	−4.11775	−	3.37935i	−0.143886	−	0.118084i
$820$	6.29994	+	1.72232i	0.220004	+	0.0601460i
$821$	7.64492	−	2.31906i	0.266810	−	0.0809358i	−0.154045	−	0.988064i	$-0.549230\pi$
$821$	7.64492	−	2.31906i	0.266810	−	0.0809358i	0.420855	+	0.907128i	$0.361730\pi$
$822$	−0.908156	−	8.07430i	−0.0316756	−	0.281624i
$823$	−38.0091	−	25.3969i	−1.32491	−	0.885279i	−0.326705	−	0.945126i	$-0.605939\pi$
$823$	−38.0091	−	25.3969i	−1.32491	−	0.885279i	−0.998208	+	0.0598476i	$0.980939\pi$
$824$	35.0464	−	16.2509i	1.22090	−	0.566129i
$825$	−14.1627	−	21.1960i	−0.493082	−	0.737950i
$826$	−2.19171	+	25.9233i	−0.0762593	+	0.901986i
$827$	−20.3516	−	24.7985i	−0.707695	−	0.862329i	0.287746	−	0.957707i	$-0.407094\pi$
$827$	−20.3516	−	24.7985i	−0.707695	−	0.862329i	−0.995441	+	0.0953777i	$0.969594\pi$
$828$	−0.519056	−	18.7617i	−0.0180385	−	0.652015i
$829$	−25.4460	+	13.6012i	−0.883776	+	0.472388i	−0.849843	−	0.527036i	$-0.823303\pi$
$829$	−25.4460	+	13.6012i	−0.883776	+	0.472388i	−0.0339328	+	0.999424i	$0.510803\pi$
$830$	−7.80554	+	12.0389i	−0.270934	+	0.417878i
$831$		−	30.2370i		−	1.04891i
$832$	−14.2494	−	22.0437i	−0.494008	−	0.764229i
$833$			14.8278i			0.513751i
$834$	−25.8932	−	16.7880i	−0.896609	−	0.581323i
$835$	−8.03673	+	4.29572i	−0.278123	+	0.148660i
$836$	40.5474	+	38.3642i	1.40236	+	1.32685i
$837$	1.01639	+	1.23848i	0.0351316	+	0.0428080i
$838$	−43.1851	−	3.65113i	−1.49180	−	0.126126i
$839$	−1.08418	−	1.62259i	−0.0374302	−	0.0560182i	0.812283	−	0.583264i	$-0.198225\pi$
$839$	−1.08418	−	1.62259i	−0.0374302	−	0.0560182i	−0.849713	+	0.527246i	$0.823225\pi$
$840$	−2.31128	−	2.12704i	−0.0797468	−	0.0733898i
$841$	39.1050	+	26.1291i	1.34845	+	0.901005i
$842$	−14.2702	+	1.60504i	−0.491783	+	0.0553132i
$843$	5.20125	−	1.57778i	0.179141	−	0.0543417i
$844$	−2.01218	−	3.52634i	−0.0692621	−	0.121382i
$845$	−1.18168	−	0.969778i	−0.0406510	−	0.0333614i
$846$	−0.0812895	−	5.87768i	−0.00279479	−	0.202079i
$847$	−12.8226	+	30.9565i	−0.440590	+	1.06368i
$848$	−16.0308	+	34.4480i	−0.550501	+	1.18295i
$849$	−0.374757	−	0.904745i	−0.0128616	−	0.0310508i
$850$	20.0021	−	8.61108i	0.686065	−	0.295358i
$851$	−0.952618	−	9.67209i	−0.0326553	−	0.331555i
$852$	−1.32363	+	18.7395i	−0.0453470	+	0.642006i
$853$	19.5996	−	36.6683i	0.671077	−	1.25550i	−0.283910	−	0.958851i	$-0.591632\pi$
$853$	19.5996	−	36.6683i	0.671077	−	1.25550i	0.954987	−	0.296646i	$-0.0958683\pi$
$854$	10.1496	+	2.92620i	0.347313	+	0.100133i
$855$	0.662155	+	3.32888i	0.0226452	+	0.113845i
$856$	−5.33674	−	37.9629i	−0.182406	−	1.29754i
$857$	41.8632	+	8.32711i	1.43002	+	0.284449i	0.848548	−	0.529118i	$-0.177477\pi$
$857$	41.8632	+	8.32711i	1.43002	+	0.284449i	0.581472	+	0.813567i	$0.302477\pi$
$858$	−24.8685	+	7.92094i	−0.848996	+	0.270416i
$859$	−5.56878	+	56.5408i	−0.190004	+	1.92915i	0.149929	+	0.988697i	$0.452095\pi$
$859$	−5.56878	+	56.5408i	−0.190004	+	1.92915i	−0.339933	+	0.940449i	$0.610405\pi$
$860$	−4.55928	−	6.43104i	−0.155470	−	0.219297i
$861$	−2.24997	+	7.41717i	−0.0766789	+	0.252777i
$862$	−43.6761	+	30.0653i	−1.48761	+	1.02403i
$863$	−4.51050	+	4.51050i	−0.153539	+	0.153539i	−0.779697	−	0.626157i	$-0.784627\pi$
$863$	−4.51050	+	4.51050i	−0.153539	+	0.153539i	0.626157	+	0.779697i	$0.284627\pi$
$864$	4.61030	+	3.27797i	0.156846	+	0.111519i
$865$	4.99927	+	4.99927i	0.169980	+	0.169980i
$866$	35.6877	+	6.58704i	1.21272	+	0.223837i
$867$	−5.22099	−	1.58377i	−0.177314	−	0.0537876i
$868$	5.07232	−	1.15564i	0.172166	−	0.0392249i
$869$	31.6091	+	3.11323i	1.07227	+	0.105609i
$870$	−3.87293	+	7.49319i	−0.131305	+	0.254043i
$871$	−3.81467	+	19.1776i	−0.129255	+	0.649809i
$872$	17.8052	+	19.9475i	0.602959	+	0.675509i
$873$	3.18120	−	0.632780i	0.107667	−	0.0214163i
$874$	31.8434	+	57.6429i	1.07712	+	1.94980i
$875$	−9.33580	−	4.99009i	−0.315608	−	0.168696i
$876$	5.37837	+	16.1119i	0.181718	+	0.544370i
$877$	21.4271	−	2.11039i	0.723543	−	0.0712627i	0.270460	−	0.962731i	$-0.412824\pi$
$877$	21.4271	−	2.11039i	0.723543	−	0.0712627i	0.453083	+	0.891469i	$0.350324\pi$
$878$	15.6647	−	39.3484i	0.528659	−	1.32795i
$879$	−1.08957	+	0.451315i	−0.0367503	+	0.0152225i
$880$	−14.9051	+	3.83237i	−0.502450	+	0.129189i
$881$	−14.9247	−	6.18203i	−0.502827	−	0.208278i	0.116828	−	0.993152i	$-0.462727\pi$
$881$	−14.9247	−	6.18203i	−0.502827	−	0.208278i	−0.619655	+	0.784874i	$0.712727\pi$
$882$	−4.30334	+	4.42404i	−0.144901	+	0.148965i
$883$	−8.34667	+	10.1705i	−0.280888	+	0.342263i	−0.894274	−	0.447521i	$-0.852307\pi$
$883$	−8.34667	+	10.1705i	−0.280888	+	0.342263i	0.613386	+	0.789784i	$0.289807\pi$
$884$	−2.79814	−	22.1194i	−0.0941116	−	0.743955i
$885$	2.24983	+	7.41671i	0.0756273	+	0.249310i
$886$	12.0467	−	15.1000i	0.404716	−	0.507295i
$887$	22.8451	−	34.1902i	0.767064	−	1.14799i	−0.218024	−	0.975943i	$-0.569961\pi$
$887$	22.8451	−	34.1902i	0.767064	−	1.14799i	0.985088	−	0.172050i	$-0.0550389\pi$
$888$	2.50096	+	1.52497i	0.0839268	+	0.0511747i
$889$	12.4571	−	8.32360i	0.417799	−	0.279164i
$890$	−3.24028	−	3.83879i	−0.108614	−	0.128676i
$891$	4.34802	−	3.56833i	0.145664	−	0.119544i
$892$	−7.09297	+	18.5598i	−0.237490	+	0.621428i
$893$	9.72243	+	18.1894i	0.325349	+	0.608684i
$894$	−8.31139	+	1.77306i	−0.277975	+	0.0593001i
$895$	−16.5354			−0.552718
$896$	16.2112	−	8.63656i	0.541579	−	0.288527i
$897$	−30.7907			−1.02807
$898$	26.5815	−	5.67063i	0.887038	−	0.189231i
$899$	−6.58544	−	12.3205i	−0.219637	−	0.410911i
$900$	8.46699	+	3.23581i	0.282233	+	0.107860i
$901$	−24.9480	+	20.4743i	−0.831139	+	0.682099i
$902$	24.4955	+	29.0200i	0.815610	+	0.966261i
$903$	7.77885	−	5.19766i	0.258864	−	0.172967i
$904$	8.41426	+	34.7086i	0.279854	+	1.15439i
$905$	−1.90122	+	2.84537i	−0.0631985	+	0.0945833i
$906$	3.39723	−	4.25828i	0.112865	−	0.141472i
$907$	−5.51176	−	18.1698i	−0.183015	−	0.603319i	−0.999657	−	0.0261754i	$-0.991667\pi$
$907$	−5.51176	−	18.1698i	−0.183015	−	0.603319i	0.816642	−	0.577144i	$-0.195833\pi$
$908$	−35.6450	+	4.50916i	−1.18292	+	0.149642i
$909$	−9.37782	+	11.4269i	−0.311043	+	0.379006i
$910$	−3.59296	+	3.69374i	−0.119106	+	0.122446i
$911$	−33.7181	−	13.9665i	−1.11713	−	0.462730i	−0.253743	−	0.967272i	$-0.581662\pi$
$911$	−33.7181	−	13.9665i	−1.11713	−	0.462730i	−0.863388	+	0.504541i	$0.831662\pi$
$912$	−19.6509	−	2.78993i	−0.650706	−	0.0923838i
$913$	−77.0774	+	31.9265i	−2.55089	+	1.05661i
$914$	9.88807	−	24.8380i	0.327068	−	0.821567i
$915$	3.13171	−	0.308447i	0.103531	−	0.0101969i
$916$	3.54787	−	1.18433i	0.117225	−	0.0391312i
$917$	1.17386	+	0.627440i	0.0387642	+	0.0207199i
$918$	2.32345	+	4.20592i	0.0766854	+	0.138816i
$919$	−39.0244	+	7.76244i	−1.28730	+	0.256059i	−0.790851	−	0.612008i	$-0.790362\pi$
$919$	−39.0244	+	7.76244i	−1.28730	+	0.256059i	−0.496446	+	0.868068i	$0.665362\pi$
$920$	−18.1269	−	1.02866i	−0.597628	−	0.0339139i
$921$	0.727234	−	3.65605i	0.0239632	−	0.120471i
$922$	−24.5753	+	47.5474i	−0.809345	+	1.56589i
$923$	30.6707	+	3.02080i	1.00954	+	0.0994309i
$924$	−4.05719	−	17.8078i	−0.133472	−	0.585835i
$925$	4.49152	+	1.36249i	0.147680	+	0.0447983i
$926$	49.9399	+	9.21762i	1.64113	+	0.302910i
$927$	9.65771	+	9.65771i	0.317201	+	0.317201i
$928$	−33.8513	−	35.8760i	−1.11122	−	1.17769i
$929$	25.1253	−	25.1253i	0.824336	−	0.824336i	−0.162391	−	0.986727i	$-0.551920\pi$
$929$	25.1253	−	25.1253i	0.824336	−	0.824336i	0.986727	+	0.162391i	$0.0519205\pi$
$930$	1.27661	−	0.878781i	0.0418617	−	0.0288164i
$931$	6.28601	−	20.7222i	0.206016	−	0.679143i
$932$	−9.34202	+	6.62303i	−0.306008	+	0.216944i
$933$	0.223052	−	2.26469i	0.00730240	−	0.0741426i
$934$	18.5285	−	5.90157i	0.606271	−	0.193105i
$935$	−12.8212	−	2.55030i	−0.419298	−	0.0834036i
$936$	5.58467	−	7.41167i	0.182541	−	0.242258i
$937$	5.80305	+	29.1739i	0.189577	+	0.953070i	0.952025	+	0.306020i	$0.0989974\pi$
$937$	5.80305	+	29.1739i	0.189577	+	0.953070i	−0.762448	+	0.647050i	$0.776003\pi$
$938$	−13.1477	−	3.79058i	−0.429289	−	0.123767i
$939$	−3.16110	+	5.91399i	−0.103158	+	0.192996i
$940$	−5.67219	−	0.400645i	−0.185006	−	0.0130676i
$941$	−1.61661	−	16.4137i	−0.0527001	−	0.535073i	−0.984899	−	0.173127i	$-0.944613\pi$
$941$	−1.61661	−	16.4137i	−0.0527001	−	0.535073i	0.932199	−	0.361945i	$-0.117887\pi$
$942$	23.1744	−	9.97682i	0.755063	−	0.325062i
$943$	17.1450	+	41.3918i	0.558319	+	1.34790i
$944$	−45.2813	−	1.94183i	−1.47378	−	0.0632012i
$945$	0.424984	−	1.02600i	0.0138247	−	0.0333758i
$946$	−0.633890	−	45.8337i	−0.0206095	−	1.49018i
$947$	41.2701	+	33.8695i	1.34110	+	1.10061i	0.986174	+	0.165714i	$0.0529929\pi$
$947$	41.2701	+	33.8695i	1.34110	+	1.10061i	0.354923	+	0.934896i	$0.384507\pi$
$948$	−9.80902	+	5.59717i	−0.318582	+	0.181788i
$949$	26.6657	−	8.08895i	0.865605	−	0.262578i
$950$	−31.6040	+	3.55465i	−1.02537	+	0.115328i
$951$	−9.89768	−	6.61342i	−0.320954	−	0.214455i
$952$	15.5889	−	0.647122i	0.505238	−	0.0209733i
$953$	−11.7030	−	17.5148i	−0.379098	−	0.567361i	0.592031	−	0.805915i	$-0.298326\pi$
$953$	−11.7030	−	17.5148i	−0.379098	−	0.567361i	−0.971129	+	0.238555i	$0.923326\pi$
$954$	−13.3857	−	1.13170i	−0.433376	−	0.0366403i
$955$	6.90284	+	8.41114i	0.223371	+	0.272178i
$956$	7.36758	−	7.78684i	0.238285	−	0.251844i
$957$	−43.2546	+	23.1201i	−1.39822	+	0.747365i
$958$	0.156611	+	0.101540i	0.00505989	+	0.00328061i
$959$		−	9.32789i		−	0.301213i
$960$	3.53539	−	4.17679i	0.114104	−	0.134805i
$961$		−	28.4331i		−	0.917198i
$962$	2.61425	−	4.03211i	0.0842868	−	0.130001i
$963$	11.9535	−	6.38925i	0.385195	−	0.205891i
$964$	56.7697	−	1.57057i	1.82843	−	0.0505847i
$965$	2.60837	+	3.17831i	0.0839663	+	0.102313i
$966$	1.81524	−	21.4705i	0.0584044	−	0.690801i
$967$	−7.68388	−	11.4997i	−0.247097	−	0.369806i	0.687101	−	0.726562i	$-0.258883\pi$
$967$	−7.68388	−	11.4997i	−0.247097	−	0.369806i	−0.934198	+	0.356755i	$0.883883\pi$
$968$	−54.8105	−	20.0827i	−1.76168	−	0.645481i
$969$	−14.0179	−	9.36643i	−0.450318	−	0.300893i
$970$	−0.350692	−	3.11796i	−0.0112600	−	0.100112i
$971$	3.03288	−	0.920014i	0.0973298	−	0.0295247i	−0.241244	−	0.970464i	$-0.577555\pi$
$971$	3.03288	−	0.920014i	0.0973298	−	0.0295247i	0.338574	+	0.940940i	$0.390055\pi$
$972$	−0.527419	+	1.92920i	−0.0169170	+	0.0618793i
$973$	−27.3855	−	22.4747i	−0.877938	−	0.720505i
$974$	28.5946	−	0.395469i	0.916229	−	0.0126716i
$975$	5.69051	−	13.7381i	0.182242	−	0.439971i
$976$	−4.36007	+	17.8782i	−0.139562	+	0.572267i
$977$	14.5845	+	35.2101i	0.466599	+	1.12647i	0.965638	+	0.259891i	$0.0836866\pi$
$977$	14.5845	+	35.2101i	0.466599	+	1.12647i	−0.499039	+	0.866580i	$0.666313\pi$
$978$	2.74567	+	6.37771i	0.0877968	+	0.203937i
$979$	−2.86307	−	29.0693i	−0.0915042	−	0.929057i
$980$	3.91368	+	4.50857i	0.125018	+	0.144021i
$981$	−4.45628	+	8.33712i	−0.142278	+	0.266184i
$982$	−3.44974	+	11.9655i	−0.110086	+	0.381835i
$983$	10.7323	+	53.9548i	0.342306	+	1.72089i	0.641870	+	0.766814i	$0.278159\pi$
$983$	10.7323	+	53.9548i	0.342306	+	1.72089i	−0.299564	+	0.954076i	$0.596841\pi$
$984$	−13.0732	−	3.38044i	−0.416757	−	0.107765i
$985$	4.79421	+	0.953627i	0.152756	+	0.0303851i
$986$	−12.7156	−	39.9216i	−0.404946	−	1.27136i
$987$	0.661452	−	6.71584i	0.0210543	−	0.213767i
$988$	−5.46671	+	32.0987i	−0.173919	+	1.02119i
$989$	15.6978	−	51.7487i	0.499161	−	1.64551i
$990$	−3.08521	−	4.48191i	−0.0980545	−	0.142444i
$991$	−15.3444	+	15.3444i	−0.487430	+	0.487430i	−0.907494	−	0.420065i	$-0.862007\pi$
$991$	−15.3444	+	15.3444i	−0.487430	+	0.487430i	0.420065	+	0.907494i	$0.362007\pi$
$992$	2.37805	+	8.74556i	0.0755032	+	0.277672i
$993$	6.76006	+	6.76006i	0.214524	+	0.214524i
$994$	−3.91458	+	21.2087i	−0.124163	+	0.672699i
$995$	−0.686723	−	0.208315i	−0.0217706	−	0.00660404i
$996$	15.7922	−	25.1114i	0.500396	−	0.795684i
$997$	45.8756	+	4.51835i	1.45290	+	0.143098i	0.793441	−	0.608647i	$-0.208287\pi$
$997$	45.8756	+	4.51835i	1.45290	+	0.143098i	0.659454	+	0.751745i	$0.270787\pi$
$998$	2.94654	+	1.52295i	0.0932710	+	0.0482080i
$999$	−0.202043	+	1.01574i	−0.00639235	+	0.0321365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.15	✓	512
128.45	even	32	inner	384.2.v.a.301.15	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.15	✓	512	1.1	even	1	trivial
384.2.v.a.301.15	yes	512	128.45	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.295054 - 1.38309i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.82589 + 0.816174i) q^{4} +(-0.528754 + 0.433938i) q^{5} +(1.08069 - 0.912200i) q^{6} +(1.34993 - 0.901992i) q^{7} +(1.66758 + 2.28455i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(-0.295054 - 1.38309i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.82589 + 0.816174i) q^{4} +(-0.528754 + 0.433938i) q^{5} +(1.08069 - 0.912200i) q^{6} +(1.34993 - 0.901992i) q^{7} +(1.66758 + 2.28455i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(0.756187 + 0.603281i) q^{10} +(1.63279 + 5.38259i) q^{11} +(-1.58052 - 1.22555i) q^{12} +(-2.08146 + 2.53627i) q^{13} +(-1.64584 - 1.60094i) q^{14} +(-0.631952 - 0.261763i) q^{15} +(2.66772 - 2.98048i) q^{16} +(3.13903 - 1.30023i) q^{17} +(1.31392 + 0.523076i) q^{18} +(-4.93809 + 0.486360i) q^{19} +(0.611277 - 1.22388i) q^{20} +(1.43184 + 0.765333i) q^{21} +(6.96285 - 3.84646i) q^{22} +(9.20414 - 1.83082i) q^{23} +(-1.22870 + 2.54760i) q^{24} +(-0.884172 + 4.44503i) q^{25} +(4.12204 + 2.13052i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-1.72863 + 2.74871i) q^{28} +(8.34413 + 2.53116i) q^{29} +(-0.175582 + 0.951282i) q^{30} +(-1.13289 - 1.13289i) q^{31} +(-4.90940 - 2.81030i) q^{32} +(-3.97733 + 3.97733i) q^{33} +(-2.72452 - 3.95793i) q^{34} +(-0.322371 + 1.06272i) q^{35} +(0.335784 - 1.97161i) q^{36} +(0.101510 - 1.03065i) q^{37} +(2.12968 + 6.68633i) q^{38} +(-3.21799 - 0.640097i) q^{39} +(-1.87309 - 0.484342i) q^{40} +(0.931377 + 4.68235i) q^{41} +(0.636056 - 2.20618i) q^{42} +(2.71639 - 5.08201i) q^{43} +(-7.37442 - 8.49535i) q^{44} +(-0.0670457 - 0.680726i) q^{45} +(-5.24791 - 12.1900i) q^{46} +(-1.59064 - 3.84015i) q^{47} +(3.88610 + 0.947729i) q^{48} +(-1.67007 + 4.03191i) q^{49} +(6.40877 - 0.0886346i) q^{50} +(2.62643 + 2.15545i) q^{51} +(1.73048 - 6.32978i) q^{52} +(-9.08984 + 2.75737i) q^{53} +(0.158067 + 1.40535i) q^{54} +(-3.19905 - 2.13754i) q^{55} +(4.31176 + 1.57983i) q^{56} +(-2.75673 - 4.12574i) q^{57} +(1.03886 - 12.2875i) q^{58} +(-7.18814 - 8.75877i) q^{59} +(1.36752 - 0.0378333i) q^{60} +(-4.05732 + 2.16868i) q^{61} +(-1.23262 + 1.90115i) q^{62} +1.62354i q^{63} +(-2.43836 + 7.61934i) q^{64} -2.24429i q^{65} +(6.67454 + 4.32748i) q^{66} +(5.25582 - 2.80929i) q^{67} +(-4.67029 + 4.93606i) q^{68} +(5.95344 + 7.25428i) q^{69} +(1.56495 + 0.132310i) q^{70} +(-5.21854 - 7.81009i) q^{71} +(-2.82599 + 0.117312i) q^{72} +(-7.06162 - 4.71842i) q^{73} +(-1.45543 + 0.163700i) q^{74} +(-4.33697 + 1.31560i) q^{75} +(8.61944 - 4.91838i) q^{76} +(7.05920 + 5.79334i) q^{77} +(0.0641671 + 4.63964i) q^{78} +(2.16094 - 5.21696i) q^{79} +(-0.117226 + 2.73357i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(6.20131 - 2.66973i) q^{82} +(1.45381 + 14.7608i) q^{83} +(-3.23902 - 0.228782i) q^{84} +(-1.09556 + 2.04964i) q^{85} +(-7.83037 - 2.25755i) q^{86} +(1.70111 + 8.55204i) q^{87} +(-9.57400 + 12.7061i) q^{88} +(-5.09328 - 1.01312i) q^{89} +(-0.921725 + 0.293581i) q^{90} +(-0.522127 + 5.30124i) q^{91} +(-15.3114 + 10.8550i) q^{92} +(0.465078 - 1.53316i) q^{93} +(-4.84195 + 3.33305i) q^{94} +(2.39999 - 2.39999i) q^{95} +(0.164185 - 5.65447i) q^{96} +(-2.29352 - 2.29352i) q^{97} +(6.06926 + 1.12023i) q^{98} +(-5.38259 - 1.63279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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